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How do you simplify a radical expression square?

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Quick Answer

To simplify a radical square root expression, identify any factor that is a perfect square, and remove it from underneath the radical sign, replacing it with its square root. For example, to simplify the square root of 63, identify that 63 is the product of 9 and 7. The square root of 9 is 3, so remove 9 from underneath the radical sign. Write the number 3 next to the square root of 7 to complete the simplification.

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Full Answer

More complex radical square root expressions feature variables represented by letters rather than numbers. The rules for simplifying such expressions are the same as those for simplifying numbers. To simplify the square root of 16y^4, identify that both 16 and y^4 are perfect squares. The square root of 16 is 4, while that of y^4 is y^2. Thus, you can eliminate the radical sign entirely, leaving you with the final answer 4y^2.

Another example is the square root of (6x - 16)^4. This problem requires identifying that (6x - 16)^4 is the same thing as (6x - 16) multiplied by itself four times, meaning the square root of the entire expression is simply (6x - 16) multiplied twice, or (6x - 16)^2.

Some problems require first multiplying two individual square root radical expressions. An example is the square root of 6 times the square root of 2. To solve this problem, first multiply 6 x 2 and place the result, 12, under the square root symbol. Then, identify that 12 = 3 x 4, with 4 being a perfect square. The final answer is 2 times the square root of 3.

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