CBSE Class 8 > Class 8 Videos > Mathematics (Maths) > Cubes & Cube Roots
Cubes & Cube Roots Video Lecture - (Maths) Class 8
FAQs on Cubes & Cube Roots Video Lecture - Mathematics (Maths) Class 8
| 1. What is a cube in mathematics? |  |
Ans. A cube in mathematics is a three-dimensional shape with equal sides and angles. It has six square faces, 12 edges, and eight vertices.
| 2. How do you calculate the volume of a cube? | |
Ans. The volume of a cube is calculated by multiplying the length of one side by itself twice. The formula for volume of a cube is V = side length x side length x side length.
| 3. What is a cube root? | |
Ans. A cube root is a number that, when multiplied by itself twice, results in the original number. For example, the cube root of 27 is 3 because 3 x 3 x 3 = 27.
| 4. How do you find the cube root of a number? | |
Ans. To find the cube root of a number, you can use the cube root symbol (∛) on a calculator or manually by finding a number that, when multiplied by itself twice, equals the original number.
| 5. What are some real-world applications of cubes and cube roots? | |
Ans. Cubes and cube roots are used in various fields such as architecture for designing buildings, engineering for calculating volumes of objects, and even in computer programming for algorithms that involve cubic functions.
Text Transcript from Video
0:0:0: you know that we use the word cube in
0:0:3: Geometry do you remember what a cube is
0:0:7: yes a cube is a three-dimensional figure
0:0:10: with six square faces and each edge of
0:0:13: the same length what is the volume of a
0:0:16: cube with side a yes it is a multiplied
0:0:19: by a multiplied by a just like this in
0:0:24: algebra cube of a number is obtained by
0:0:26: multiplying the same number three times
0:0:30: for example cube of 2 is equal to 2 into
0:0:33: 2 into 2 = to 8 and of 3 is 3 into 3
0:0:37: into 3 equal to
0:0:40: 27 let's study about a perfect Cube it
0:0:44: is a number which can be obtained by
0:0:46: cubing a natural number for example 8 is
0:0:49: a perfect Cube as it is obtained by
0:0:52: cubing two 27 is a perfect Cube as it is
0:0:56: obtained by cubing three let's calculate
0:0:59: cu cubes of some
0:1:1: numbers let's start with four what will
0:1:4: it be to calculate cube of four we will
0:1:8: multiply 4 three times therefore 4 Cub
0:1:12: is equal to 4 into 4 into 4 4 into 4 is
0:1:16: 16 and 16 into 4 is finally
0:1:20: 64 try the next on your own 5 so cube of
0:1:26: 5 is 5 into 5 into 5 is 12
0:1:30: 25 let's see a different type of
0:1:33: question if you calculate the cube of
0:1:36: any number which has one at its one's
0:1:38: place what do you think will be the
0:1:40: digit on one's place of the cube correct
0:1:43: it will be one similarly if you
0:1:46: calculate the cube of any number which
0:1:49: has two at its one's place it will have
0:1:51: the digit at one's Place equal to 8 so
0:1:55: the digit at the one's place in the cube
0:1:58: of any number is equal to the cube of
0:2:0: the digit at the one's place of the
0:2:2: original number let's try a question
0:2:6: find the one's digit of the cube of each
0:2:9: of the following numbers
0:2:12: 31 yes the answer is one because the
0:2:16: digit at one's place of the number is
0:2:18: one and a cube of one is equal to 1
0:2:22: let's confirm by calculating its Cube so
0:2:25: the cube of 31 is 31 into 31 into 31
0:2:29: which using calculator comes out to be
0:2:33: 29791 now let's try
0:2:36: 53 what do you think is the answer what
0:2:39: is the digit at one's place of this
0:2:42: number it is three and what is the cube
0:2:45: of three yes it is
0:2:48: 27 so what will be the
0:2:51: answer yes the digit at once place is
0:2:54: seven now moving on let's see some
0:2:57: interesting patterns the first is adding
0:3:0: consecutive odd
0:3:2: numbers let's observe this is the list
0:3:5: of consecutive odd
0:3:7: numbers let's take one first one is
0:3:10: itself a perfect cube next we take the
0:3:14: next two three and 5 the sum is eight
0:3:17: and it is a perfect cube of two the sum
0:3:20: of next 3 7 9 11 comes out to be 27 and
0:3:25: it is also the cube of three and hence
0:3:28: is a perfect Cube
0:3:30: the second pattern is about cubes and
0:3:33: their prime
0:3:34: factors consider the following prime
0:3:36: factorization of the numbers and the
0:3:39: cubes each prime factor appears three
0:3:42: times in its
0:3:43: cubes now we'll see how to judge whether
0:3:47: a number is a perfect Cube or not is 216
0:3:51: a perfect Cube let's do it together
0:3:55: first step is to make prime factors of
0:3:57: the number that is
0:4:0: 216 / 2 is 108 / 2 is 54 ided 2 is
0:4:7: 27 27 / 3 is 9 ided 3 gives us 3 so we
0:4:14: get the prime factors of 216 equal to 2
0:4:18: into 2 into 2 into 3 into 3 into 3 so
0:4:23: let's check if 216 is a perfect Cube or
0:4:27: not it is a perfect Cube
0:4:30: why because in the prime factors of 216
0:4:35: we observe each prime number occurring
0:4:37: in the multiple of three times 216 is
0:4:41: equal to 2 Cub * 3 Cub so to check
0:4:46: whether a number is a perfect Cube or
0:4:48: not always make prime factors out of it
0:4:51: and then judge let's try checking 392
0:4:56: also first let's find prime factors of
0:5:1: 392 392 ided 2 gives
0:5:5: 196 divided by 2 gives us 98 / 2 gives
0:5:9: us
0:5:11: 49 49 / 7 gives us 7 so the prime
0:5:17: factors of 392 equal to 2 into 2 into 2
0:5:21: into 7 into 7 is it a perfect Cube let's
0:5:26: check the first Factor two
0:5:30: how many two are there yes there are
0:5:33: three in number so it passes the
0:5:37: criteria the second Factor seven how
0:5:41: many seven are there yes there are two
0:5:44: in number so it fails the
0:5:47: criteria this implies 392 is not a
0:5:51: perfect Cube now we have a question what
0:5:55: smallest number to multiply with 392 to
0:5:59: make it a perfect Cube can you think of
0:6:2: any
0:6:3: number yes it is seven we need to
0:6:7: multiply 7 into 392 to make it a perfect
0:6:11: Cube how did we see it because 7 was a
0:6:16: number which did not pass the criteria
0:6:18: and it was two in number rather should
0:6:20: be in multiple of three so the minimum
0:6:23: number we can multiply in 392 to make it
0:6:27: a perfect cube is 7
0:6:30: next concept we have is cube
0:6:32: roots imagine you have a cube volume of
0:6:37: the cube is 125 M Cub you need to find
0:6:41: the length of the side of the cube we
0:6:44: know the formula for the volume of a
0:6:46: cube that is side Cube to find the
0:6:50: length of the cube we need to know which
0:6:52: number has its Cube equal to
0:6:55: 125 so we need to find the cube root of
0:7:0: 125 and the number whose cube is equal
0:7:3: to 125 is 5 so cube root of 125 is 5 so
0:7:11: cube root of number is a value which
0:7:13: when multiplied by itself thce or three
0:7:16: times produces the original value let's
0:7:20: find the cube root of
0:7:23: 3,375 again the first step is
0:7:27: factorization let us factorize 30
0:7:30: 375
0:7:32: 3375 / 3 we get 1125 / 3 gives
0:7:37: 375 divided by 3 we get
0:7:42: 125 125 ided 5 we get 25 and divided by
0:7:48: 5 gives 5 so the prime factors of
0:7:52: 3,375 are equal to 3 into 3 into 3 into
0:7:56: 5 into 5 into 5 equal to 3 Cub into 5
0:8:0: Cub now to get the cube root we remove
0:8:4: the three from the powers of the
0:8:6: numbers so we get 3 into 5 that is
0:8:11: 15 this implies cube root of
0:8:15: 3375 is equal to 15 we hope that you
0:8:20: have understood the concept of cubes and
0:8:22: cube
0:8:23: roots now here's a secret on how you can
0:8:26: study effectively with the urv app you
0:8:29: can learn with chapter notes watch video
0:8:32: lectures and solve ncer based McQ tests
0:8:36: of this chapter on
0:8:37: urv and that's not all you also get
0:8:40: amazing courses for Class 8 and much
0:8:43: more for your class 8
0:8:45: preparation thank you
0:0:3: Geometry do you remember what a cube is
0:0:7: yes a cube is a three-dimensional figure
0:0:10: with six square faces and each edge of
0:0:13: the same length what is the volume of a
0:0:16: cube with side a yes it is a multiplied
0:0:19: by a multiplied by a just like this in
0:0:24: algebra cube of a number is obtained by
0:0:26: multiplying the same number three times
0:0:30: for example cube of 2 is equal to 2 into
0:0:33: 2 into 2 = to 8 and of 3 is 3 into 3
0:0:37: into 3 equal to
0:0:40: 27 let's study about a perfect Cube it
0:0:44: is a number which can be obtained by
0:0:46: cubing a natural number for example 8 is
0:0:49: a perfect Cube as it is obtained by
0:0:52: cubing two 27 is a perfect Cube as it is
0:0:56: obtained by cubing three let's calculate
0:0:59: cu cubes of some
0:1:1: numbers let's start with four what will
0:1:4: it be to calculate cube of four we will
0:1:8: multiply 4 three times therefore 4 Cub
0:1:12: is equal to 4 into 4 into 4 4 into 4 is
0:1:16: 16 and 16 into 4 is finally
0:1:20: 64 try the next on your own 5 so cube of
0:1:26: 5 is 5 into 5 into 5 is 12
0:1:30: 25 let's see a different type of
0:1:33: question if you calculate the cube of
0:1:36: any number which has one at its one's
0:1:38: place what do you think will be the
0:1:40: digit on one's place of the cube correct
0:1:43: it will be one similarly if you
0:1:46: calculate the cube of any number which
0:1:49: has two at its one's place it will have
0:1:51: the digit at one's Place equal to 8 so
0:1:55: the digit at the one's place in the cube
0:1:58: of any number is equal to the cube of
0:2:0: the digit at the one's place of the
0:2:2: original number let's try a question
0:2:6: find the one's digit of the cube of each
0:2:9: of the following numbers
0:2:12: 31 yes the answer is one because the
0:2:16: digit at one's place of the number is
0:2:18: one and a cube of one is equal to 1
0:2:22: let's confirm by calculating its Cube so
0:2:25: the cube of 31 is 31 into 31 into 31
0:2:29: which using calculator comes out to be
0:2:33: 29791 now let's try
0:2:36: 53 what do you think is the answer what
0:2:39: is the digit at one's place of this
0:2:42: number it is three and what is the cube
0:2:45: of three yes it is
0:2:48: 27 so what will be the
0:2:51: answer yes the digit at once place is
0:2:54: seven now moving on let's see some
0:2:57: interesting patterns the first is adding
0:3:0: consecutive odd
0:3:2: numbers let's observe this is the list
0:3:5: of consecutive odd
0:3:7: numbers let's take one first one is
0:3:10: itself a perfect cube next we take the
0:3:14: next two three and 5 the sum is eight
0:3:17: and it is a perfect cube of two the sum
0:3:20: of next 3 7 9 11 comes out to be 27 and
0:3:25: it is also the cube of three and hence
0:3:28: is a perfect Cube
0:3:30: the second pattern is about cubes and
0:3:33: their prime
0:3:34: factors consider the following prime
0:3:36: factorization of the numbers and the
0:3:39: cubes each prime factor appears three
0:3:42: times in its
0:3:43: cubes now we'll see how to judge whether
0:3:47: a number is a perfect Cube or not is 216
0:3:51: a perfect Cube let's do it together
0:3:55: first step is to make prime factors of
0:3:57: the number that is
0:4:0: 216 / 2 is 108 / 2 is 54 ided 2 is
0:4:7: 27 27 / 3 is 9 ided 3 gives us 3 so we
0:4:14: get the prime factors of 216 equal to 2
0:4:18: into 2 into 2 into 3 into 3 into 3 so
0:4:23: let's check if 216 is a perfect Cube or
0:4:27: not it is a perfect Cube
0:4:30: why because in the prime factors of 216
0:4:35: we observe each prime number occurring
0:4:37: in the multiple of three times 216 is
0:4:41: equal to 2 Cub * 3 Cub so to check
0:4:46: whether a number is a perfect Cube or
0:4:48: not always make prime factors out of it
0:4:51: and then judge let's try checking 392
0:4:56: also first let's find prime factors of
0:5:1: 392 392 ided 2 gives
0:5:5: 196 divided by 2 gives us 98 / 2 gives
0:5:9: us
0:5:11: 49 49 / 7 gives us 7 so the prime
0:5:17: factors of 392 equal to 2 into 2 into 2
0:5:21: into 7 into 7 is it a perfect Cube let's
0:5:26: check the first Factor two
0:5:30: how many two are there yes there are
0:5:33: three in number so it passes the
0:5:37: criteria the second Factor seven how
0:5:41: many seven are there yes there are two
0:5:44: in number so it fails the
0:5:47: criteria this implies 392 is not a
0:5:51: perfect Cube now we have a question what
0:5:55: smallest number to multiply with 392 to
0:5:59: make it a perfect Cube can you think of
0:6:2: any
0:6:3: number yes it is seven we need to
0:6:7: multiply 7 into 392 to make it a perfect
0:6:11: Cube how did we see it because 7 was a
0:6:16: number which did not pass the criteria
0:6:18: and it was two in number rather should
0:6:20: be in multiple of three so the minimum
0:6:23: number we can multiply in 392 to make it
0:6:27: a perfect cube is 7
0:6:30: next concept we have is cube
0:6:32: roots imagine you have a cube volume of
0:6:37: the cube is 125 M Cub you need to find
0:6:41: the length of the side of the cube we
0:6:44: know the formula for the volume of a
0:6:46: cube that is side Cube to find the
0:6:50: length of the cube we need to know which
0:6:52: number has its Cube equal to
0:6:55: 125 so we need to find the cube root of
0:7:0: 125 and the number whose cube is equal
0:7:3: to 125 is 5 so cube root of 125 is 5 so
0:7:11: cube root of number is a value which
0:7:13: when multiplied by itself thce or three
0:7:16: times produces the original value let's
0:7:20: find the cube root of
0:7:23: 3,375 again the first step is
0:7:27: factorization let us factorize 30
0:7:30: 375
0:7:32: 3375 / 3 we get 1125 / 3 gives
0:7:37: 375 divided by 3 we get
0:7:42: 125 125 ided 5 we get 25 and divided by
0:7:48: 5 gives 5 so the prime factors of
0:7:52: 3,375 are equal to 3 into 3 into 3 into
0:7:56: 5 into 5 into 5 equal to 3 Cub into 5
0:8:0: Cub now to get the cube root we remove
0:8:4: the three from the powers of the
0:8:6: numbers so we get 3 into 5 that is
0:8:11: 15 this implies cube root of
0:8:15: 3375 is equal to 15 we hope that you
0:8:20: have understood the concept of cubes and
0:8:22: cube
0:8:23: roots now here's a secret on how you can
0:8:26: study effectively with the urv app you
0:8:29: can learn with chapter notes watch video
0:8:32: lectures and solve ncer based McQ tests
0:8:36: of this chapter on
0:8:37: urv and that's not all you also get
0:8:40: amazing courses for Class 8 and much
0:8:43: more for your class 8
0:8:45: preparation thank you
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Feb 16, 2026 Last updated
Video Description: Cubes & Cube Roots for Class 8 2026 is part of Mathematics (Maths) Class 8 preparation. The notes and questions for Cubes & Cube Roots have been prepared according to the Class 8 exam syllabus. Information about Cubes & Cube Roots covers all important topics for Class 8 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Cubes & Cube Roots.
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