EZ Math

Algebra 2 · Rational exponents and radicals

How to Simplify a Square Root

Problem

72\sqrt{72}

Answer

626\sqrt{2}

A simplified square root has no square factor left under the radical. Look for the largest perfect square that divides the number.

Step-by-step solution

  1. Find the largest perfect square that divides 72.

    72=36×272 = 36 \times 2

    Why: Pulling out the largest square keeps the leftover root as small as possible.

  2. Split the root across the product.

    72=36×2\sqrt{72} = \sqrt{36} \times \sqrt{2}

    Why: The square root of a product is the product of the square roots.

  3. Simplify the perfect square.

    626\sqrt{2}

    Why: The square root of 36 is 6, and 2 has no square factor left.

Common mistakes

  • Writing 36 sqrt(2). Take the root of the perfect square.
  • Using 4 x 18 instead of 36 x 2, which leaves another square factor to pull out.
  • Adding 6 and 2 to get 8.

Practice problems

Use the same method. Work each problem on paper, then open the answer to check.

  1. 50\sqrt{50}

    Show answer

    525\sqrt{2}

  2. 18\sqrt{18}

    Show answer

    323\sqrt{2}

  3. 48\sqrt{48}

    Show answer

    434\sqrt{3}

  4. 32\sqrt{32}

    Show answer

    424\sqrt{2}

  5. 75\sqrt{75}

    Show answer

    535\sqrt{3}