Simplifying Radicals Math Example 5

Follow the full solution, then compare it with the other examples linked below.

Example 5

medium
Simplify 1825\sqrt{\frac{18}{25}}.

Solution

  1. 1
    1825=1825=325\sqrt{\frac{18}{25}} = \frac{\sqrt{18}}{\sqrt{25}} = \frac{3\sqrt{2}}{5}.
  2. 2
    Since 18=9×218 = 9 \times 2 and 9=3\sqrt{9} = 3.

Answer

325\frac{3\sqrt{2}}{5}
The quotient rule for radicals lets you separate numerator and denominator: a/b=a/b\sqrt{a/b} = \sqrt{a}/\sqrt{b}. Then simplify each part.

About Simplifying Radicals

Simplifying a radical means rewriting it so no perfect-square factor remains under the root sign. For example, √50 = √(25·2) = 5√2. The result — called simplified radical form — has the smallest possible number under the radical.

Learn more about Simplifying Radicals →

More Simplifying Radicals Examples

Example 1 easy

Simplify [formula].

Example 2 medium

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Example 3 medium

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Example 4 easy

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