## RS Aggarwal Class 8 Chapter 4 Assertion Reason Cube and Cube Roots Solutions

**Cubes and Cube Roots**

**Assertion- Reason Questions**

**Directions (Questions 1 to 5): Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:**

**(a.) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).**

**(b.) Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).**

**(c.) Assertion (A) is true but Reason (R) is false.**

**(d.) Assertion (A) is false but Reason (R) is true.**

**1.) Assertion (A):** (1(1/5)^{3}=1(1/125)

**Reason (R):** To find the cube of a mixed fraction, we need to convert it into an important fraction before finding its cube.

Ans: Option (d) is the correct answer as the assertion A is false but the reason R is true.

[1(1/5)]^{3}= (6/5)^{3}= 216/125= 1(91/125)

So we can clearly see that A is false but R is true.

**2.) Assertion (A):** 3^{3}>3, (10)^{3}>10, (6/5)^{3}> 6/5

**Reason (R):** The cube of a rational number is always greater than the number.

Ans: Option (c) is the correct answer as the assertion A is true and the reason R is false.

3^{3}= 27>3; 10^{3}= 1000>10; (6/5)^{3}= 216/125> 6/5

So, A is true.

The cube of a rational number greater than 1 is greater than the number while the cube of a rational number less than 1 is smaller than the number. So, R is false.

**3.) Assertion (A):** Each one of (11)^{3}, (17)^{3} and (19)^{3} has only 3 factors in all.

**Reason (R):** The cube of a prime number always has 3 factors in all namely, 1, the prime number and the number itself.

Ans: Option (a) is correct answer as the assertion A is true and the reason R is true.

11^{3}=11×11×11,

17^{3}=17×17×17,

19^{3}=19×19×19

We can clearly see that 11^{3}, 17^{3} and 19^{3} has three prime factors so the assertion A is true.

**4.) Assertion (A):** [(-1)^{3} × 2^{3} ×(-3)^{3} × 4^{3}] is a positive number.

**Reason (R):** The cube of a negative number is negative while that of a positive number is positive.

Ans: Option (a) is the correct answer as the assertion A is true and the reason R is also true.

(-1)^{3} × 2^{3} × (-3)^{3} ×4^{3}= (-ve) × (+ve) × (-ve) ×(+ve)= (+ve) so we can see that A is true.

It is clear that reason R is also true.

**5.) Assertion (A):** If x and y are integers such that x^{2}>y^{2} then x^{3}> y^{3}

**Reason (R):** Squares of negative integers are positive while their cubes are negative.

Ans: Option (d) is correct answer as the assertion A is false and the reason R is true.

Let x= -2 and y = -1.

Then, x^{2}= (-2)^{2}=4 and y^{2}= (-1)^{2}=1. So, x^{2}>y^{2}

But, X^{3}= (-2)^{3}=-8 and y^{3}= (-1)^{3}= -1. So, x^{3} <y^{3}.

So, A is false. But R is true.