Cubes & Cube Roots Video Lecture | Mathematics (Maths) Class 8

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
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0:8:40: amazing courses for Class 8 and much
0:8:43: more for your class 8
0:8:45: preparation thank you