Today’s ACT question of the day is a great math question about simplifying radicals.  There are two approaches: a calculator approach, and a non-calculator approach.

The question: what integer approximates ?

The calculator approach needs little explanation. Take the square root of each expression (7.07, 8.94), then multiply them together and round to the nearest integer (63).  This matches C perfectly.

The non-calculator approach:

50 * 80 = 4000, so we need to find √4000. 60^2 is 3600, so we know the answer has to be a little bit more than 60.

Non-calculator approach #2:

Simplify √50 into √(25 *2) = 5√2.  √2 is roughly 1.4, so this is about 7.

Simplify √80 into √(16 * 5) = 4√5. √5 is roughly 2.2, so this is about 8.8, or roughly 9.

7 * 9 = 63

It can pay to know rough approximations of common square roots, especially √2 since it appears in so many triangles.