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Class 8 Exam  >  Class 8 Tests  >  Test: Cubes And Cube Roots- 2 - Class 8 MCQ

Test: Cubes And Cube Roots- 2 - Class 8 MCQ


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30 Questions MCQ Test - Test: Cubes And Cube Roots- 2

Test: Cubes And Cube Roots- 2 for Class 8 2024 is part of Class 8 preparation. The Test: Cubes And Cube Roots- 2 questions and answers have been prepared according to the Class 8 exam syllabus.The Test: Cubes And Cube Roots- 2 MCQs are made for Class 8 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Cubes And Cube Roots- 2 below.
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Test: Cubes And Cube Roots- 2 - Question 1
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If 73 = 343, then ∛343 = _________.

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Test: Cubes And Cube Roots- 2 - Question 2
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What will be the unit digit of the cube of a number ending with 6 ?

Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 2

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Test: Cubes And Cube Roots- 2 - Question 3
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Each prime factor appears _________ times in its cube.

Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 3

True
If a3 is the cube and m is one of the prime factors of a. Then, m appears three times in a3.

Test: Cubes And Cube Roots- 2 - Question 4
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What will be the unit digit of the cube of a number ending with 2 ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 4
- To find the unit digit of a number ending in 2 when cubed, we can simply cube the unit digit 2.
- The calculation is: 2 x 2 x 2 = 8.
- Therefore, the unit digit of the cube of any number ending with 2 is 8.
- This means if you take a number like 12, 22, or 52, their cubes will all have a unit digit of 8.
Test: Cubes And Cube Roots- 2 - Question 5
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The number of digits in the cube root of a 6-digit number is _______.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 5

As 1003 = 1000000 which is the smallest 3 digit number. So it’s only 2 digit number which is the cube root of a 6 digit number

Test: Cubes And Cube Roots- 2 - Question 6
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The expansion of a3 is ___________.
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Test: Cubes And Cube Roots- 2 - Question 7
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What will be the unit digit of the cube root of a number ends with 3?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 7

for example like 343 so its cube root will be 7
because 73 will always have 3 as unit digit

Test: Cubes And Cube Roots- 2 - Question 8
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The smallest natural number by which 135 must be divided to obtain a perfect cube is
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 8

 we have 135 =  3 x 3 x 3 x 5

Grouping the prime factors of 135 into triples, we are left over with 5.
∴  135 is not a perfect cube
Now, [135]divided by5 = [ 3 x 3 x 3 x 5] divided by5
or  27 = 3 x 3 x 3
i.e. 27 is a perfect cube.
Thus, the required smallest number is 5

Test: Cubes And Cube Roots- 2 - Question 9
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What will be the unit digit of ∛216
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 9
We can find it by Prime Factorization method 
³√216 = 2×2×2×3×3×3 
= 2 and 3 are making triplets i.e. 2 and 3 
= 2×3 = 6 Thus, we can say that 6 i.e option 'B' is correct.
Test: Cubes And Cube Roots- 2 - Question 10
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The value of ∛343 is-
Test: Cubes And Cube Roots- 2 - Question 11
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What is the volume of a cube whose edge is 2cm ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 11
Volume of cube=2×2×2=8
Test: Cubes And Cube Roots- 2 - Question 12
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Which of the following is Hardy-Ramanujan Number ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 12
This story is very famous among mathematicians. 1729 is sometimes called the “Hardy-Ramanujan number”.
There are two ways to say that 1729 is the sum of two cubes. 1x1x1=1; 12x12x12=1728. So 1+1728=1729 But also: 9x9x9=729; 10x10x10=1000. So 729+1000=1729 There are other numbers that can be shown to be the sum of two cubes in more than one way, but 1729 is the smallest of them.
Ramanujan did not actually discover this fact. It was known in 1657 by a Frenchmathematician Bernard Franicle de Bessy.

But it got famous after the ramanujans above conversation.

So it's famously known as Ramanujan Number.

Test: Cubes And Cube Roots- 2 - Question 13
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The value of 53 is __________.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 13

Raising 5 to the power of 3 is 

Test: Cubes And Cube Roots- 2 - Question 14
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How many zeros will be there in the cube root of 800?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 14

Since in cubes the zeros become triple ,for instance 10*10*10=1000, a number with two zeros does not have a cube root.

Test: Cubes And Cube Roots- 2 - Question 15
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By which smallest natural number 392 must be multiplied so as to make the product a perfect cube ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 15


392 = 2 × 2 × 2 × 7 × 7
Hence the number should be multiplied by 7 to make it a perfect cube.

Test: Cubes And Cube Roots- 2 - Question 16
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The cube of an even number is always ____________.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 16

The cube of an even number is always an even number. Here's why:

Test: Cubes And Cube Roots- 2 - Question 17
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729 is the value of  _______________.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 17

To find the value of 729729729, we check cube powers:

Test: Cubes And Cube Roots- 2 - Question 18
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The cube of an odd number is always __________.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 18

The cube of an odd number is always an odd number because:

Test: Cubes And Cube Roots- 2 - Question 19
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The smallest natural number by which 243 must be multiplied to make the product a perfect cube  is __________. 
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Test: Cubes And Cube Roots- 2 - Question 20
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How many zeros will be there in the cube root of 27000?
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Test: Cubes And Cube Roots- 2 - Question 21
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Which of the following is a perfect cube ?
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Test: Cubes And Cube Roots- 2 - Question 22
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What will be the unit digit of the cube of a number ending with 4 ?
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Test: Cubes And Cube Roots- 2 - Question 23
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For a number ending with 7, the unit digit of its cube is equal to:
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 23

If the unit digit is 7, the cube will have unit digit as 7×7×7 = 343

So, the unit digit will be 3.

Test: Cubes And Cube Roots- 2 - Question 24
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Which of the following is not a perfect cube ?
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 24

To determine which of the following numbers is not a perfect cube, we need to check whether the number can be expressed as the cube of an integer.

  • a) 1 is a perfect cube because 1=13.
  • b) 9 is not a perfect cube. The cube root of 9 is not an integer.
  • c) 8 is a perfect cube because 8 = 23.
  • d) 27 is a perfect cube because 27 = 33.

Thus, the number that is not a perfect cube is:

b) 9.

Test: Cubes And Cube Roots- 2 - Question 25
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The cube root of 512 is ________.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 25

Test: Cubes And Cube Roots- 2 - Question 26
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9 is the cube root of  __________.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 26

9 is the cube root of  729 because 9 x 9 x 9 = 729

So option B is correct answer. 

Test: Cubes And Cube Roots- 2 - Question 27
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If 83 = 512, then ∛512 = _______
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 27

8*8*8 =512

Test: Cubes And Cube Roots- 2 - Question 28
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The smallest natural number by which 704 must be divided to obtain a perfect cube is
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Test: Cubes And Cube Roots- 2 - Question 29
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What will be the unit digit of the cube root of a number ends with 2?
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Test: Cubes And Cube Roots- 2 - Question 30
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The cube of 4 is _______________.
Detailed Solution for Test: Cubes And Cube Roots- 2 - Question 30

The cube of 4 is:

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