Question

1. which of these numbers is a perfect square? how do you know? a) 14 b) 60 c) 36

Explanation:

Step1: Recall perfect square definition

A perfect square is a number that can be expressed as \( n^2 \), where \( n \) is an integer.

Step2: Check option a (14)

Find integers \( n \) such that \( n^2 = 14 \). The square of 3 is \( 3^2 = 9 \), and the square of 4 is \( 4^2 = 16 \). Since 14 is between 9 and 16 and not a square of an integer, 14 is not a perfect square.

Step3: Check option b (60)

Find integers \( n \) such that \( n^2 = 60 \). The square of 7 is \( 7^2 = 49 \), and the square of 8 is \( 8^2 = 64 \). Since 60 is between 49 and 64 and not a square of an integer, 60 is not a perfect square.

Step4: Check option c (36)

Find an integer \( n \) such that \( n^2 = 36 \). We know that \( 6^2 = 36 \) (since \( 6\times6 = 36 \)), so 36 can be expressed as the square of the integer 6. Thus, 36 is a perfect square.

Answer:

c) 36 is a perfect square because \( 6^2 = 36 \), meaning it can be written as the square of the integer 6.