# Question Video: Solving Quadratic Equations Involving Geometric Formulas Mathematics • 8th Grade

The formula for the area of a square is 𝐴 = 𝑠², where 𝑠 is the side length. Estimate the side length of a square whose area is 74 square inches.

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### Video Transcript

The formula for the area of a square is 𝐴 equals 𝑠 squared, where 𝑠 is the side length. Estimate the side length of a square whose area is 74 square inches.

So why is the area of a square equal to 𝑠 squared? Well, we can think of the area of a square as length times width. However, the length and the width are the exact same length. That’s why they’re all labelled 𝑠; they’re all equal in measure. So length times width is actually 𝑠 times 𝑠. That’s how we get 𝑠 squared.

This question is asking us to estimate the side length of the square whose area is 74 square inches. So let’s go ahead and plug in 74 for the area.

Now we need to estimate 𝑠. So in order to do that, we need to solve for 𝑠. So we need to get rid of the squared. The inverse operation of squaring would be to square root. So let’s go ahead and square root both sides of the equation. The square root of 74, we will leave as the square root of 74 because we’re going to be estimating that. And the square root of 𝑠 squared is equal to 𝑠.

So in order to estimate the square root of 74, let’s place it on a number line. Here we can see the square root of 74 is between the square root of 64 and the square root of 81. The largest perfect square less than 74 is the square root of 64 and that is equal to eight. And the smallest perfect square greater than 74 is the square root of 81 and that’s nine.

So the square root of 74 is between eight and nine. Since the square root of 74 is closer to the square root of 81 than it is to the square root of 64, the best whole number estimate for the square root of 74 would be nine.

This means nine inches would be our estimate for the side length of the square.