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Find each square root. Where necessary, round to the nearest 100 th:

sqrt((32)/(50))

Find each square root. Where necessary, round to the nearest $100$ th: $\newline$ $\sqrt{\frac{32}{50}}$

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Roots of rational numbers

Full solution

Q. Find each square root. Where necessary, round to the nearest

100

th:

\newline

\sqrt{\frac{32}{50}}

Apply Quotient Rule: Apply the quotient rule of radicals to $\sqrt{\frac{32}{50}}$ . $\sqrt{\frac{32}{50}} = \frac{\sqrt{32}}{\sqrt{50}}$
Find Square Roots: Find the square root of the numerator and denominator separately. $\newline$ $\sqrt{32} = \sqrt{16 \times 2} = 4 \times \sqrt{2}$ $\newline$ $\sqrt{50} = \sqrt{25 \times 2} = 5 \times \sqrt{2}$
Divide Square Roots: Divide the square roots we found. $\newline$ $(\sqrt{32})/(\sqrt{50}) = (4 \times \sqrt{2}) / (5 \times \sqrt{2})$
Simplify Expression: Simplify the expression by canceling out $\sqrt{2}$ . $\frac{4 \times \sqrt{2}}{5 \times \sqrt{2}} = \frac{4}{5}$

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