Video: Finding the Area of a Square Given That Its Side Length Is an Irrational Number

Find the area of a square whose side length is 7√5 cm.

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Video Transcript

Find the area of a square whose side length is seven square root five centimeters.

So here we have a square. And we know the side length is seven square root five centimeters. But in a square, all sides are equal. So we can label them all seven square root five centimeters. So we are supposed to find the area. And the formula for the area of a square is equal to the length times the width. Or since we know that the length and the width are equal, we could just call it a side length.

So the side length times the side length would be equal to the side length squared. So we could find the area either way. Let’s begin with the length times the width, so seven square root five times seven square root five.

When multiplying with square roots, we multiply the numbers outside of the square root together. So seven times seven is 49. And then we multiply numbers inside the square root together. So square root five times square root five is square root 25.

Now the square root of 25 simplifies to be five. So 49 times five gives us an area of 245 centimeters squared. Now if we would use the other formula, we should get the exact same answer. So using the side length squared, we take seven square root five and we square it.

So we need to square the number on the outside of the square root and square the number with the square root. So we have seven squared times square root five squared. Seven squared is equal to 49. Now the square root of five squared is technically just five, because if we square a square root, the square root will disappear. Or if we would’ve squared the number on the inside of the square root, we would have the square root of 25, which again is five. So 49 times five gives us 245. So like we said, the area of this square will be 245 squared centimeters.

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