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If and are nonnegative, the square root of the product is equal to the product of the square roots of and
Given a square root radical expression, use the product rule to simplify it.
Simplify the radical expression.
Simplify
Notice the absolute value signs around x and y ? That’s because their value must be positive!
Given the product of multiple radical expressions, use the product rule to combine them into one radical expression.
Simplify the radical expression.
Just as we can rewrite the square root of a product as a product of square roots, so too can we rewrite the square root of a quotient as a quotient of square roots, using the quotient rule for simplifying square roots. It can be helpful to separate the numerator and denominator of a fraction under a radical so that we can take their square roots separately. We can rewrite as
The square root of the quotient is equal to the quotient of the square roots of and where
Given a radical expression, use the quotient rule to simplify it.
Simplify the radical expression.
Simplify
We do not need the absolute value signs for because that term will always be nonnegative.
Simplify the radical expression.
We can add or subtract radical expressions only when they have the same radicand and when they have the same radical type such as square roots. For example, the sum of and is However, it is often possible to simplify radical expressions, and that may change the radicand. The radical expression can be written with a in the radicand, as so
Given a radical expression requiring addition or subtraction of square roots, solve.
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