Question

Square roots and Cube roots can be rational or irrational. The square root of a rational square (√7 = 2.6457...) is always irrational. The square root of a perfect (√25 = 5) is a rational, whole number. This means that √36 is rational and √10 is irrational.

Answer 1

Actually, the given statement is incorrect. Let's break it down:

1. Square root of a rational square: The square root of any rational number squared will always be a rational number. For example, √(2^2) = √4 = 2, which is a rational number.

2. Square root of a perfect square: The square root of any perfect square will always be a whole number, which is a rational number. For example, √(5^2) = √25 = 5, which is a rational number.

Therefore, √36 is rational because it is the square root of a perfect square, and √10 is irrational because it cannot be expressed as a fraction of two integers.