JSS2: MATHEMATICS - 1ST TERM
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Properties of Whole Numbers I | Week 14 Topics|1 Quiz
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Properties of Whole Numbers II | Week 24 Topics|1 Quiz
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Properties of Whole Numbers III | Week 35 Topics|1 Quiz
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Indices | Week 42 Topics|1 Quiz
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Laws of Indices | Week 55 Topics|1 Quiz
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Whole Numbers & Decimal Numbers | Week 64 Topics|1 Quiz
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Standard Form | Week 73 Topics|1 Quiz
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Significant Figures (S.F) | Week 84 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages I | Week 96 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages II | Week 104 Topics|1 Quiz
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Fractions, Ratios, Proportions & Percentages III | Week 113 Topics|1 Quiz
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Approximation & Estimation | Week 121 Topic|1 Quiz
Square Root of Fractions
Topic Content:
- Square Root of Fractions
To find the square roots of fractions, reduce fractions to their lowest terms to have perfect squares for both the numerator and denominator.
Worked Example 3.3.1:
Find the value of the following
a. \(\sqrt{ \frac{9 }{25}} \)
b. \(\sqrt{ \frac{49 }{4}} \)
c. \(\sqrt{ \frac{18 }{72}} \)
d. \(\sqrt{\scriptsize 2 \normalsize \frac{1 }{4}} \)
e. \(\sqrt{ \frac{72 }{50}} \)
f. \(\sqrt{ \frac{48 }{108}} \)
Solution
a. \(\sqrt{ \frac{9 }{25}} \\ = \frac{\sqrt{9}}{\sqrt{25}}\\ = \frac{3}{5}\)
b. \(\sqrt{ \frac{49 }{4}}\\ = \frac{\sqrt{49}}{\sqrt{4}}\\ = \frac{7}{2}\)
c. \(\sqrt{ \frac{18 }{72}} \\= \frac{\sqrt{2 \: \times \: 9}}{\sqrt{2 \: \times \: 36}} \\ = \frac{\sqrt{9}}{\sqrt{36}}\\= \frac{3}{6} \\ = \frac{1}{2}\)
d. \(\sqrt{\scriptsize 2 \normalsize \frac{1}{4}} \\ = \sqrt{ \frac{9 }{4}} \\= \frac{\sqrt{9}}{\sqrt{4}} \\ = \frac{3}{2} \\ = \scriptsize 1 \normalsize \frac{1}{2}\)
e. \(\sqrt{ \frac{72 }{50}} \\= \frac{\sqrt{2 \: \times \: 36}}{\sqrt{2 \: \times \: 25}}\\ =\sqrt{ \frac{36 }{25}}\\= \frac{6}{5} \\ = \scriptsize 1 \normalsize \frac{1}{5} \)
f. \(\sqrt{ \frac{48}{108}}\\ = \frac{\sqrt{2 \: \times \: 24}}{\sqrt{2 \: \times \: 54}}\\ =\sqrt{ \frac{24 }{54}}\\ =\sqrt{ \frac{12 }{27}}\\ = \frac{\sqrt{4 \: \times \: 3}}{\sqrt{9 \: \times \: 3}}\\ = \sqrt{ \frac{4 }{9}}\\ = \frac{2}{3}\)