Question

1 does a square with an area of 20 cm² have a whole-number side length? explain why. determine whether each number is a non-perfect square number

Explanation:

Step1: Recall the area formula for a square

The area \( A \) of a square is given by the formula \( A = s^2 \), where \( s \) is the length of a side.

Step2: Solve for the side length

Given \( A = 20 \, \text{cm}^2 \), we solve for \( s \) by taking the square root of both sides: \( s=\sqrt{20} \).

Step3: Simplify and analyze the square root

Simplify \( \sqrt{20} \): \( \sqrt{20}=\sqrt{4\times5} = \sqrt{4}\times\sqrt{5}=2\sqrt{5}\approx2\times2.236 = 4.472 \). A whole number is an integer (e.g., 0, 1, 2, 3, ...). Since \( 4.472 \) is not an integer, the side length is not a whole number.

Answer:

No, a square with an area of \( 20 \, \text{cm}^2 \) does not have a whole - number side length. The side length \( s=\sqrt{20}\approx4.472 \), which is not an integer (whole number).