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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 100100 th:\newline3250 \sqrt{\frac{32}{50}}

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Full solution

Q. Find each square root. Where necessary, round to the nearest 100100 th:\newline3250 \sqrt{\frac{32}{50}}
  1. Apply Quotient Rule: Apply the quotient rule of radicals to 3250\sqrt{\frac{32}{50}}.3250=3250\sqrt{\frac{32}{50}} = \frac{\sqrt{32}}{\sqrt{50}}
  2. Find Square Roots: Find the square root of the numerator and denominator separately.\newline32=16×2=4×2\sqrt{32} = \sqrt{16 \times 2} = 4 \times \sqrt{2}\newline50=25×2=5×2\sqrt{50} = \sqrt{25 \times 2} = 5 \times \sqrt{2}
  3. Divide Square Roots: Divide the square roots we found.\newline(32)/(50)=(4×2)/(5×2)(\sqrt{32})/(\sqrt{50}) = (4 \times \sqrt{2}) / (5 \times \sqrt{2})
  4. Simplify Expression: Simplify the expression by canceling out 2\sqrt{2}.4×25×2=45\frac{4 \times \sqrt{2}}{5 \times \sqrt{2}} = \frac{4}{5}

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