Video: Using Square Roots to Solve Word Problem Involving Areas of Squares

Given that the area of each square on the chessboard is 21 cm², find the length of the chessboard’s sides.

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Video Transcript

Given that the area of each square on the chessboard is 21 centimetres squared, find the length of the chessboard’s sides.

So if the area of each square is 21, centimetres squared to be exact, then each side length will be the square root of 21 because the area of a square is just equal to the side length squared. So the side length times the side length. So if we know the area is 21, then we set 𝑆 squared equal to 21. We square root both sides and find that the side length is equal to the square root of 21.

So if this side of the square is equal to the square root of 21, each of these squares are equal, so each one will have a side length that is the square root of 21. So in order to find the entire side length of the big square, we’ll need to add them all together. And there are eight of them, so the square of 21 added together eight times or just eight multiplied to the square root of 21. Therefore, the side length would be eight square root 21 centimetres.

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