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Perfect Square Factors

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 1 of 40.

$A square with sides 5 and a dashed diagonal marked with a question mark$

A square tile has sides of 5 cm. Its diagonal is $\sqrt{50}$ cm, about 7.07 cm. The exact length is $5\sqrt{2}$ . You get it like this, because 50 = 25 · 2.

$\sqrt{50} = \sqrt{25}\cdot \sqrt{2} = 5\sqrt{2}$

25 is a perfect square: 5 times 5. Take out the largest perfect square, and you are done in one step.

Challenge

Simplify $\sqrt{72}$ by taking out the largest perfect square. First write it as two roots multiplied. Then write it in simplest form, with no perfect square left inside.

Try it yourself

\sqrt{72}

Write it in simplest radical form

All lessons in Radicals & Rational Exponents

1Simplest Form

Perfect Square FactorsLike Radicals Simplify First Recap: Adding Radicals

4Rationalizing

One Root Below A Number and a Root The Conjugate Below Recap: Rationalizing

7Powers and Roots Equations

Odd Powers Even Powers Fractional Powers Two Thirds Power Recap: Power Equations

2Letters and Cube Roots

Letters Under the Root Cube Roots Recap: Simplifying Radicals

5Rational Exponents

One Over n m Over n Negative Exponents Exponent Rules Still Work Recap: Rational Exponents

8Radical Functions

Domain of a Root Evaluating Inverse of a Square Recap: Radical Functions

3Multiplying Radicals

Root Times Root Distributing a Root Two Brackets Conjugate Pairs Recap: Multiplying Radicals

6Radical Equations

Square Both Sides Isolate the Root First A False Answer Cube Root Equations Recap: Radical Equations

9Final Challenges

Final: Simplify and Add Final: Clear the Root Final: The Exponent Final: Check It Final: The Falling Ball