Question

In the following equations, find whether X, Y, Z represents rational or irrational:

1. x² = 125
2. y⁴ = 625
3. z² = 196

Answer 1

X is irrational because the square root of 125 is not a perfect square, while Y and Z are rational because the fourth root of 625 is 5, and the square root of 196 is 14, respectively.

Step-by-step explanation:

To determine whether X, Y, and Z represent rational or irrational numbers, we must solve each equation and examine the solutions:

1. x² = 125: To find x, take the square root of both sides. The square root of 125 is not a perfect square, so x is an irrational number.
2. y⁴ = 625: To find y, take the fourth root of both sides. The fourth root of 625 is 5, because 5⁴=625. Therefore, y is a rational number.
3. z² = 196: To find z, take the square root of both sides. The square root of 196 is 14 since 14²=196. Hence, z is a rational number.

So, X is irrational, while Y and Z are rational.