Math  /  Numbers & Operations

Question\begin{align*} \text{a) } & \frac{75}{5 \sqrt{3}} ; \frac{42}{7 \sqrt{2}} ; \frac{18}{3 \sqrt{2}} ; \frac{45}{5 \sqrt{3}} ; \frac{36}{4 \sqrt{3}} ; \frac{24}{2 \sqrt{6}} ; \frac{6}{3 \sqrt{2}} ; \frac{15}{\sqrt{3}}; \\ \text{b) } & \frac{28}{4 \sqrt{7}} ; \frac{24}{4 \sqrt{6}} ; \frac{18}{6 \sqrt{3}} ; \frac{36}{6 \sqrt{6}} ; \frac{54}{9 \sqrt{6}} ; \frac{72}{9 \sqrt{8}} ; \frac{30}{15 \sqrt{2}} ; \frac{42}{6 \sqrt{7}}; \\ \text{c) } & \frac{8}{3 \sqrt{2}} ; \frac{6}{\sqrt{3}} ; \frac{24}{5 \sqrt{6}} ; \frac{15}{2 \sqrt{3}} ; \frac{4}{3 \sqrt{2}} ; \frac{28}{3 \sqrt{7}} ; \frac{12}{5 \sqrt{2}} ; \frac{10}{3 \sqrt{5}}; \\ \text{d) } & \frac{12}{5 \sqrt{6}} ; \frac{15}{5 \sqrt{3}} ; \frac{18}{\sqrt{24}} ; \frac{25}{4 \sqrt{5}} ; \frac{15}{2 \sqrt{5}} ; \frac{30}{7 \sqrt{6}} ; \frac{45}{2 \sqrt{10}} ; \frac{8}{3 \sqrt{6}} ; \frac{9}{2 \sqrt{6}}; \\ \text{e) } & \frac{18}{2 \sqrt{6}} ; \frac{45}{5 \sqrt{3}} ; \frac{3}{\sqrt{12}} ; \frac{9}{\sqrt{27}} ; \frac{12}{\sqrt{48}} ; \frac{24}{10 \sqrt{6}} ; \frac{15}{3 \sqrt{6}} ; \frac{18}{3 \sqrt{54}}. \end{align*}

Studdy Solution
Continue simplifying each fraction in the list using the same method.
Example: For 1832\frac{18}{3 \sqrt{2}}:
1832×22=1823×2=1826=32\frac{18}{3 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{18 \sqrt{2}}{3 \times 2} = \frac{18 \sqrt{2}}{6} = 3 \sqrt{2}
Repeat the above steps for all fractions in groups b), c), d), and e) until all fractions are simplified.

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