Simplifying surds
Simplify the surd — take everything you can out of the root.
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The surd √72 can be written more simply. We split 72 so that one factor is a square: 72 = 36 · 2. The square root of 36 is 6, so √72 = 6√2. This is called simplifying a surd (in the US: simplest radical form).
What does this generator do?
On the easy level you simplify square roots like √72 or √180. On the medium level cube roots appear (∛54 = 3∛2), as well as surds with a number in front (3√50 = 15√2). On the hard level there is a variable under the root too, for example √(18a³) = 3a√(2a).
How to use it
1) Find the largest square (for a cube root, the largest cube) that divides the radicand. 2) Take its root and write it in front of the root sign. 3) Leave the rest under the root. In the first box write the number in front of the root, in the second the number under it.