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 quotient rule for simplifying square roots
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.
Write the radical expression as the quotient of two radical expressions.
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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