Square Root of Decimals

To find the square root of decimals, change the decimals to fractions.

Worked Example 3.4.1:

Evaluate the following:

1. \( \scriptsize \sqrt {0.25} \)

2. \( \scriptsize \sqrt {0.64} \)

3. \( \scriptsize \sqrt {0.36} \)

4. \( \scriptsize \sqrt {12.25} \)

5. \( \scriptsize \sqrt {0.25 \: \times \: 0.64} \)

Solution

1. \( \scriptsize \sqrt {0.25} \\= \sqrt{\normalsize \frac{25 }{100}} \\ = \normalsize \frac{5}{10} \\ = \scriptsize 0.5 \)

2. \( \scriptsize \sqrt {0.64} \\ = \sqrt{\normalsize \frac{64 }{100}}\\ = \normalsize\frac{8}{10} \\ = \scriptsize 0.8 \)

3. \( \scriptsize \sqrt {0.36} \\= \sqrt{\normalsize \frac{36 }{100}}\\ = \normalsize\frac{6}{10} \\ =\scriptsize 0.6 \)

4. \( \scriptsize \sqrt {12.25}\\ = \sqrt{ \normalsize\frac{1225 }{100}}\\ = \sqrt{ \normalsize\frac{49 \: \times \: 25 }{4 \: \times \: 25}} \\ = \sqrt{ \frac{49 }{4}} \\= \frac{7}{2} \\ = \scriptsize 3 \normalsize \frac{1}{2} \)

5. \( \scriptsize \sqrt {0.25 \: \times \:0.64} \\ = \sqrt{\normalsize \frac{25 }{100}} \: \times \: \sqrt{\normalsize \frac{64 }{100}}\\ = \frac{5}{10} \: \times\: \frac{8}{10} \\= \frac{40}{100}\\ = \frac{4}{10} \\ = \scriptsize 0.4 \)