CUBE AND CUBE ROOTS

EXERCISE 4 (A)

 

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

(i) The cube root of 8000 is 200.

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

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

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

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

2.Find the cubes of the following numbers.

(i) 8

(ii) ​\( -15 \)​

(iii) 600

3.

(i) ​ ​\( \dfrac{5}{6} \)​

(ii) \( \dfrac{-7}{9} \) 

(iii) ​\( 1\dfrac{3}{5} \)​

4.

(i) 0.03

(ii) 1.7

(iii) ​\( -0.008 \)​

5.Which of the following numbers are perfect cubes?

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

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

(i) 5832

(ii) 91125

(iii) ​\( -9261 \)​

(iv) ​\( \dfrac{125}{343} \)​

(v) ​\( -\dfrac{2744}{4096} \)​

(vi) ​\( -5\dfrac{104}{125} \)​

7.Evaluate:

(i) ​\( \sqrt[3]{1.331} \)​

(ii) ​\( \sqrt[3]{0.003375} \)​

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

(ii) 6912

(iii) 47916

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

(ii) 1458

(iii) 120393

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