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Properties of Whole Numbers I | Week 14 Topics1 Quiz
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Properties of Whole Numbers II | Week 24 Topics1 Quiz
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Properties of Whole Numbers III | Week 35 Topics1 Quiz
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Indices | Week 42 Topics1 Quiz
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Laws of Indices | Week 55 Topics1 Quiz
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Whole Numbers & Decimal Numbers | Week 64 Topics1 Quiz
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Standard Form | Week 73 Topics1 Quiz
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Significant Figures (S.F) | Week 84 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages I | Week 96 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages II | Week 104 Topics1 Quiz
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Fractions, Ratios, Proportions & Percentages III | Week 113 Topics1 Quiz
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Approximation & Estimation | Week 121 Topic1 Quiz
Topic Content:
- Worked Examples – Square Root of Fractions
- Evaluation Questions
Worked Example 3.5.1:
Solve the following:
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. Evaluate the following
1. \( \scriptsize \sqrt{25 \: \div \: 9} \)
2. \( \scriptsize \sqrt{49 \: \div \: 4} \)
3. \( \scriptsize \sqrt{9 \: +\: 16} \)
4. \( \scriptsize \sqrt{80 \: + \: 30 \: – \: 46} \)
5. \( \scriptsize \sqrt{12 \: -\: 3} \)
6. \( \scriptsize \sqrt{1 \: +\: 6 \: \times \: 4} \)
7. \( \scriptsize \sqrt{64 \: -\: 7\: \times \: 4} \)
View AnswersB. Find the squares of the following:
1. \( \left( \scriptsize 2 \frac{1}{2} \right)^2 \)
2. \( \left( \scriptsize 1.5 \right)^2 \)
3. \( \left( \frac{4}{5} \right)^2 \)
4. \( \left( \frac{1}{2} \: +\: \frac{3}{2} \right)^2 \)
5. \( \left( \frac{3}{4}\right)^2 \: +\: \left(\frac{4}{5} \right)^2 \)
6. \( \left( \scriptsize 2.5 \right)^2 \)
7. \( \left( \scriptsize 0.3 \right)^2 \)
8. \( \left( \frac{9}{10} \right)^2 \)
View AnswersC. 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. \( \sqrt{ \scriptsize 7 \frac{1}{9}} \)
View AnswersD. 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. \(\scriptsize \sqrt{0.0001} \)
View Answers