# 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) ​$$\sqrt[3]{0.003375}$$

(i) 1125

(ii) 6912

(iii) 47916

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

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