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S.chand books class 8 maths solution chapter cube and cube roots

EXERCISE 4 (A)


Question 1

Write (T) for True or (F) for false:

(i) The cube root of 8000 is 200.

Sol: False

(ii) Each prime factor appears 3 times in its cube.

Sol: True

(iii) ​\sqrt[3]{27+64}=\sqrt[3]{27}+\sqrt[3]{64}​.

Sol: False

(iv) For an integer a, ​a^3​ is always greater than ​a^2​.

Sol: False

(v) The least number by which 72 must be divided to make it a perfect cube is 9.

Sol: True


Question 2

Find the cubes of the following numbers.

(i) 8

Sol: 8×8×8

=512

(ii) -15

Sol: (-15)×(-15)×(-15)

= -3375

(iii) 600

Sol:600×600×600

= 216000000


Question 3

(i) ​ ​\dfrac{5}{6}

Sol: =\dfrac{5}{6} \times \dfrac{5}{6} \times \dfrac{5}{6}=\dfrac{5\times5\times 5}{6\times 6\times 6}

=\dfrac{125}{216}


(ii) \dfrac{-7}{9} 

Sol:=\dfrac{-7}{9} \times \dfrac{-7}{9} \times \dfrac{-7}{9}=

=

(iii) ​1\dfrac{3}{5}

Sol:=1\dfrac{3}{5} \times 1\dfrac{3}{5} \times 1\dfrac{3}{5}=

=


Question 4

(i) 0.03

Sol: 0.03×0.03×0.03

=

(ii) 1.7

Sol: 1.7×1.7×1.7

=

(iii) ​ -0.008

Sol: -0.008×0.008×0.008

=


Question 5

Which of the following numbers are perfect cubes?

65, 128, 243, 512, 900, 1728, 4096

Sol:


Question 6

Find the cube root of the following numbers by prime factorization method.

(i) 5832

Sol:

(ii) 91125 

Sol:

(iii) ​ -9261

Sol:

(iv) ​\dfrac{125}{343}

Sol:

(v) ​-\dfrac{2744}{4096}

Sol:

(vi) ​-5\dfrac{104}{125}

Sol:


Question 7

Evaluate:

(i) ​\sqrt[3]{1.331}

Sol:

(ii) ​\sqrt[3]{0.003375}

Sol:


Question 8

What is the smallest number by which each of the following numbers must be multiplied so that the product is a perfect cube.Also, find cube root of the product.

(i) 1125

Sol:

(ii) 6912

Sol:

(iii) 47916

Sol:


Question 9

Find the smallest number by which each of the following numbers must be divided so that quotient is a perfect cube. Also, find the cube root of the product.

(i) 3584

Sol:

(ii) 1458

Sol:

(iii) 120393

Sol:


Question 10

Find the value of :

(i) ​\sqrt[3]{27}+\sqrt[3]{0.008}+\sqrt[3]{0.064}

(ii) ​\bigg\{(5^2+\sqrt{10^2})\bigg\}^3

(iii) ​\sqrt[3]{686}\times\sqrt[3]{500}

 

 

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