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When simplifying square roots investigate if the number can be converted into factors any or all of which are perfect squares. The square root(s) of these factors can then be readily obtained.
√54 = √(9 x 6) = √9 x √6 = 3√6
This process can be taken further if required.
√54 = √(9 x 4 x 1.5) = √9 x √4 x √1.5 = (3 x 2)√1.5 = 6√1.5
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What is the difference between estimating a square root and simplifying a square root?
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.
What is the square root of 212 simplified?
The square root of 212 simplified is: 14.6
What Is the square root of 13 simplified?
The square root of 13 simplified is 3.6
What is the square root of 20 simplified as?
The square root of 20 is simplified as: ± 4.5
What is the simplified square root of 530000?
The simplified square root of 530,000 is: ± 728
