Lesson 3, Topic 4
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# Evaluation Questions – Square Root of Fractions

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Example

a. $$\sqrt {\frac{25}{64}}\: \div\: \sqrt {\frac{48}{108}}$$

b. $$\sqrt {\frac{1}{36}} \:\div \:\sqrt {\frac{4}{16}}$$

c. $$\sqrt {\frac{36 \: \times \: 98}{32}}$$

Solution

a. $$\sqrt {\frac{25}{64}}\: \div\: \sqrt {\frac{48}{108}} \\= \sqrt {\frac{5 \: \times \: 5}{8 \: \times \: 8}}\: \div\: \sqrt {\frac{3 \: \times \: 16 }{3 \: \times \: 36}} \\ = \sqrt {\frac{5 \: \times \: 5}{8 \: \times \: 8}}\: \div\: \sqrt {\frac{16 }{36}} \\ =\sqrt {\frac{5 \: \times \: 5}{8 \: \times \: 8}}\: \div\: \sqrt {\frac{4 \: \times \: 4 }{6 \: \times \: 6}}\\ = \frac{5}{8} \: \div \: \frac{4}{6}\\ = \frac{5}{8} \: \times \: \frac{6}{4} \\= \frac{30}{32} \\=\frac{15}{16}$$

b. $$\sqrt {\frac{1}{36}} \:\div \: \sqrt {\frac{4}{16}}\\ = \frac{1}{6} \: \div \: \frac{2}{4}\\ = \frac{1}{6} \: \times \: \frac{4}{2} \\=\frac{1}{3}$$

c. $$\sqrt {\frac{36 \: \times \: 98}{32}} \\= \sqrt {\frac{36 \: \times \: 2 \; \times \: 49}{16 \: \times \: 2}} \\= \sqrt {\frac{36 \: \times \: 49}{16}}\\ = \frac{6 \: \times \: 7}{4}\\ = \frac{3 \: \times \: 7}{2} \\= \frac{21}{2} \\ = \scriptsize 10 \normalsize \frac{1}{2}$$

Evaluation Questions

A. Find the value of the following:

1. $$\sqrt{ \frac{81}{64}}$$

2. $$\sqrt{ \frac{18}{200}}$$

3. $$\sqrt {\frac{72}{450}}$$

4. $$\sqrt {\frac{1}{36} }$$

5. $$\sqrt {\frac{4}{100}}$$

6. $$\sqrt{ \scriptsize 3 \frac{1}{16}}$$

7. $$\sqrt{ \scriptsize 6 \frac{1}{4}}$$

8. $$\sqrt{ \scriptsize 7 \frac{1}{9}}$$

B. Evaluate the following:

1. $$\sqrt{\frac{4}{100} \: \times \: \frac{18}{8}}$$

2. $$\sqrt{\frac{16}{25} \: \div \: \frac{25}{64}}$$

3. $$\sqrt{\frac{18}{8} \: \div \: \frac{4}{16}}$$

4. $$\scriptsize \sqrt{0.5625}$$

5. $$\scriptsize \sqrt{2.25}$$

6. $$\scriptsize \sqrt{48 \: \div \: 3}$$

7. $$\scriptsize \sqrt{0.0049}$$

8. $$\scriptsize \sqrt{0.0001}$$

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