Question

find square roots
study the example showing how to find square roots.
then solve problems 1–5.
example
garrett puts square patches together to make square quilts. each patch has an area of 1 ft². which areas listed below are possible areas of the square quilts garrett can make? what will be the side length of each square quilt?
area 8 ft² area 16 ft² area 18 ft² area 25 ft²
you can use square tiles or grid paper to solve.
area 5 ft² not possible area 18 ft² not possible
area 16 ft² grid of 4x4 squares area 25 ft² grid of 5x5 squares
a quilt with area 16 ft² has side length 4 ft, and a quilt with area 25 ft² has side length 5 ft.
1 explain how you could check the answer to the example.

2 laqueta says that because −4 multiplied by itself equals 16, this means that −4 is also a solution to the problem in the example. do you agree or disagree? explain.

vocabulary
square root of x: a number that when multiplied by itself equals x

Explanation:

Question 1

To check the answer, we use the formula for the area of a square, \( A = s^2 \), where \( A \) is the area and \( s \) is the side length. For the quilt with area \( 16 \, \text{ft}^2 \), substitute \( s = 4 \) into the formula: \( A = 4^2 = 16 \), which matches the given area. For the quilt with area \( 25 \, \text{ft}^2 \), substitute \( s = 5 \): \( A = 5^2 = 25 \), which also matches. This confirms the side lengths are correct.

We disagree. In the context of the problem, the side length of a quilt (a physical object) represents a length, and length cannot be negative. Even though \( (- 4)\times(-4)=16 \), the side length of a quilt must be a positive quantity, so \( - 4 \) is not a valid solution for the side length of the quilt.

Answer:

To check, use the square - area formula \( A = s^2 \). For the \( 16 \, \text{ft}^2 \) quilt, \( 4^2 = 16 \), and for the \( 25 \, \text{ft}^2 \) quilt, \( 5^2 = 25 \), which match the areas, so the side lengths are correct.

Question 2