The Largest Square

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 3 of 43.

√(48) has several square factors: 4, and also 16. Splitting off 4 gives √(4) × √(12), which is 2√(12). That is not finished, because 12 still holds a 4. A second step gives 2 × 2√(3), which is 4√(3).

Splitting off the largest square, 16, gets there at once: √(16) × √(3), which is 4√(3). Both routes end at the same number, since they are the same root. The largest square just leaves nothing behind to check.

To find it, try the squares from the top down: 49, 36, 25, 16, 9, 4. The first one that divides the number is the largest. And when you are done, check what is left inside: if it still has a square factor, you have one more step.

Challenge

Simplify √(72) in one step by splitting off the largest perfect square. Type the product of two roots, then the simplified form. The board accepts a line only if it equals the one above.

Try it yourself

sqrt(72)

Write it in simplest radical form