Perfect Square Factors

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 2 of 43.

To simplify √(12), look for a perfect square that divides 12. 4 does, since 12 is 4 times 3. Split the root over that product, then take the square root of the square:

√(12) = √(4) × √(3) = 2√(3)

Why this works: √(4) is a whole number, so it leaves the root sign, and the 3 has no square inside it, so it stays. 2√(3) means 2 times √(3), and it is the same number as √(12): square it and you get 4 times 3, which is 12.

The perfect squares to try are 4, 9, 16, 25, 36, 49 and so on. For √(63), 9 divides 63, so it is √(9) × √(7), which is 3√(7).

Challenge

Simplify √(50). Type each next line: first √(50) as a product of two roots, the first a perfect square, then that square's root times the root that is left. The board accepts a line only if it equals the one above.

Try it yourself

sqrt(50)

Write it in simplest radical form