Right Triangles – Square Roots

Square Roots

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Students learn to simplify square roots. For example, to simplify the square root of 16, since 4 squared is 16, the square root of 16 is 4. Note that 16 is a perfect square, so its square root is an integer. To simplify the square root of a number that is not a perfect square, such as 45, first find the prime factorization of the number, in this case 3 times 3 times 5. Next, since the 3's pair up, a 3 comes out of the radical, and since the 5 does not pair up, it stays inside the radical. So the square root of 45 simplifies to 3 times the square root of 5.
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