Tutoring high school math, you see this a few times each semester. The tutor shows an example.

Suppose you get asked a question like the following:

Example: Simplify √(0.225)

Unless you have one of those new-style calculators, perhaps the WriteView or the natural display, you might likely receive just a decimal.

If you need exact form, here’s how to do it by hand:

1. Rewrite the question in fraction form:

√(0.225) = √(225/1000)

2. Reduce the fraction inside:

√(225/1000) = √(9/40)

3. Write the radical separately top and bottom (which doesn’t change the value, but can make the problem simpler to consider)

√(9/40) = √(9)/√(40)

4. Take the square root of top and bottom separately, or else simplify:

√(9)/√(40) = 3/(√(4)√(10) )= 3/(2√(10))

5. Rationalize the denominator; in this case, multiply top and bottom by √(10) to remove the radical from the denominator.

(3√(10))/(2√(10)√(10))

Since √(10) times √(10) = 10, the expression becomes

(3√(10))/20

Math: simplifying decimal radicals