AI Tutor
Quick test: what is 0.4\sqrt{0.4}? If your instinct said 0.20.2, try multiplying 0.2×0.20.2 \times 0.2 — you get 0.040.04, not 0.40.4!
Decimals inside radicals trip up almost everyone because multiplying decimals doubles the count of decimal places.
Let's explore two reliable methods that eliminate the guesswork and make simplifying decimal square roots effortless.

The Fraction Conversion Method

The most foolproof way to simplify a decimal radical is to rewrite the radicand — the expression inside the root — as a fraction over a power of 10.
Because roots distribute across division via the quotient property (ab=ab\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}), powers of 10 with an even number of zeros (100,10,000100, 10{,}000) become whole-number denominators instantly.
What happens if the decimal has an odd number of decimal digits, like 0.80.8 or 0.0080.008?

Odd Decimal Places and Imperfect Squares

If you convert 0.80.8 directly, you get 810\sqrt{\frac{8}{10}}, but 1010 is not a perfect square.
To make the denominator an easy perfect square, multiply the top and bottom by 1010 to make it 80100\sqrt{\frac{80}{100}} before simplifying.
Watch out for a classic trap: 0.9\sqrt{0.9} is not 0.30.3, because 0.32=0.090.3^2 = 0.09. Instead, 0.9=90100=31010\sqrt{0.9} = \sqrt{\frac{90}{100}} = \frac{3\sqrt{10}}{10}.