Simplifying Radicals Math Example 1

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

Example 1

easy
Simplify 72\sqrt{72}.

Solution

  1. 1
    Step 1: Find the largest perfect square factor: 72=36×272 = 36 \times 2.
  2. 2
    Step 2: 72=36×2=36⋅2=62\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \cdot \sqrt{2} = 6\sqrt{2}.
  3. 3
    Check: 62×2=726^2 \times 2 = 72 ✓

Answer

626\sqrt{2}
To simplify a radical, factor the radicand into a perfect square times a remaining factor. Extract the square root of the perfect square part. The goal is to have no perfect square factors under the radical.

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 2 medium

Simplify [formula].

Example 3 medium

Simplify [formula].

Example 4 easy

Simplify [formula].

Example 5 medium

Simplify [formula].

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