Cube and Cube Roots Class 8 MCQ Questions

Answer: (a) 0.001331

Explanation: When we need to find the Cube of a Decimal number, we find the cube of the number after the decimal point. Note that the number of digits on the right side of decimal point is triple the number of digits on the right of the decimal in the number whose cube is being found

In this question there are two digit on the right of the decimal so in its cube there will be three digits at the right of decimal point.

Cube of 11 = 11 x 11 x 11

= 1331

Now we shall put in the value 1331 on the right side of the Decimal. Since the number of digit in 1331 is 4 we would add decimals before 6 digits.

Hence (0.11)³ =0.001331

Answer: (b) 1000

Explanation: In order to find Cube of an Natural Number, we simply multiplying a number by itself 3 times

(10)³= 10 x 10 x 10

= 1000

Answer: (c) 27000

Explanation: In order to find Cube of an Natural Number, we simply multiplying a number by itself 3 times

It must be noted that Cube of an Even Number is always Even.

(30)³ = 30 x 30 x 30

= 27000

Answer: (b) 79507

Explanation: In order to find Cube of an Natural Number, we simply multiplying a number by itself 3 times

It must noted that cube of a odd number is always odd

(43)³ = 43 x 43 x 43

= 79507

Answer: (b) -22

Explanation: To find the cube root of any given number, we will first do the prime factorization of such number

Prime factorization of a Perfect Cube will always give us product of triplets.

Thereafter we will choose one digit from each triplet and multiply them amongst themselves

Factorizing -10648 we get

-10648 = – ( 2 x 2 x 2 x 11 x 11 x 11 )

Taking one digit from each triplet and multiplying them

3√−10648 = – ( 2 x 11 )

= -22

Answer: (c) 90

Explanation: In such a case, we will factorize each of the integers separately and choose one digit from the product of triplets.

3√(729×1000) = (3√729) x(3√1000)

√A×B = √A x √B

= √(9×9×9)x √(10×10×10)

= (9³)^1/3 x (10³)^1/3 Since (3√a) =(a)^1/3

= (9^3×(1/3)) ×(10^3×(1/3))   (a^m)ⁿ = a^{m n}

= 9¹ x 10¹

= 9 x 10

= 90

Answer: (b) 68

Explanation: To find the cube root of any given number, we will first do the prime factorization of such number

Prime factorization of a Perfect Cube will always give us product of triplets.

Thereafter we will choose one digit from each triplet and multiply them amongst themselves

Factorizing 314432 we get:

314432 = 2 x 2 x 2 x 2 x 2 x 2 x 17 x 17 x 17

Taking one digit from each triplet and multiplying them

√314432 = 2 x 2 x 17

√314432 = 68

Answer: (b) 6/5

Explanation: We will Factorise both Numerator and Denominator

3√216/125 = 3√216/3√125 Since 3√A/B = 3√A/3√B

= 3√(6×6×6)/3√(5×5×5)

= (6³/5³)^1/3 Since 3√a=(a)^1/3

= (6^3×(1/3))/5^3×(1/3)  (a^m)ⁿ = a^{m n}

= 6¹/5¹

= 6/5

Answer: (b) 25

Explanation: A number is a perfect Cube, if it can be expressed as a Product of Triplets

To convert any number into a perfect cube, we would need to do Prime factorisation of the given number. If the prime factors, form triplets, the number would be a perfect cube. If one or more factors do not form triplets, we would divide each such factors by factors to eliminate the numbers not forming Triplets.

We can write

675 = 3 x 3 x 3 x 5 x 5

In the given question, while 3 x 3 x 3 forms a Triplet but there are only two 5s

To make the given number a Perfect Cube we have to divide the given number by 5 x 5 i.e. 25

Answer: (b) 6

Explanation: A number is a perfect Cube, if it can be expressed as a Product of Triplets

To convert any number into a perfect cube, we would need to do Prime factorisation of the given number. If the prime factors, form triplets, the number would be a perfect cube. If one or more factors do not form triplets, we would multiply each such factors by additional factors to make them Triplets.

We can write

36000 = 10 x 10 x 10 x 6 x 6

In the given question, while 10 forms a Triplet there are only two 6’s

To make it a perfect cube, we have to multiply the number by 6 as this is the only number which is not expressed as a product of triplet.

Answer: (a) Yes

Explanation: A number is a perfect Cube, if it can be expressed as a Product of Triplets

To find whether any number is a perfect cube or not, we would need to do Prime factorization of the given number. If the prime factors, form triplets, the number would be a perfect cube. If one or more factors do not form triplets, the numbers would not be a perfect Cube.

Rewriting 2744 into prime factors

2744 = 14 X 14 X 14

We can see that while one triplet is formed for the number 14 and there are no other factors.

Hence the given number is a Perfect Cube.