Perfect Squares, Cubes and Roots

Perfect Squares, Cubes and Roots

Perfect squares and cubes are useful landmarks. A square number has equal rows and columns; a cube number has equal length, width and height. Square and cube roots reverse those structures. Estimate unfamiliar roots between nearby perfect values instead of expecting every root to be a whole number.

Worked example

$\sqrt{144}=12$ because $12^2=144$. Since $11^2=121$ and $12^2=144$, $\sqrt{130}$ lies between 11 and 12.

Exam method

1. Recall or build a nearby power table. 2. State the root that undoes the power. 3. Check by raising your answer to the matching power.