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Example: The square root of 54

The square root of 54 is not an integer, since 54 is not a perfect square. The square root of 54 will be between 7 and 8, since 54 is between 49 and 64. Since 54 is closer to 49 than it is to 64, the square root will be closer to 7 than 8. I'd estimate the square root of 54 to be approximately 7.35

The actual square root is plus or minus 7.3484692

To simplify a square root, search for any factors greater than one that are perfect squares. Since 54 = 9 x 6, the square root of 54 equals the square root of 9 x 6 equals the square root of 9 times the square root of 6. The square root of 9 is 3, so the square root of 54 simplified is 3 times the square root of 6.

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Q: What is the difference between estimating a square root and simplifying a square root?
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