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Find each square root. Where necessary, round to the nearest 100th: sqrt((2)/(25))

Find each square root. Where necessary, round to the nearest 100100th:\newline225 \sqrt{\frac{2}{25}}

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Full solution

Q. Find each square root. Where necessary, round to the nearest 100100th:\newline225 \sqrt{\frac{2}{25}}
  1. Apply Quotient Rule: First, apply the quotient rule of radicals to 225\sqrt{\frac{2}{25}}.\newline225=225\sqrt{\frac{2}{25}} = \frac{\sqrt{2}}{\sqrt{25}}
  2. Find Square Roots: Now, find the square root of the numerator and denominator separately. 2\sqrt{2} is an irrational number, so we'll leave it as is for now. 25=5×5=5\sqrt{25} = \sqrt{5 \times 5} = 5
  3. Calculate Decimal Value: So we have: 225=25\sqrt{\frac{2}{25}} = \frac{\sqrt{2}}{5}
  4. Divide to Get Answer: Since we need to round to the nearest hundredth, let's use a calculator to find the decimal value of 2\sqrt{2}.2≈1.41\sqrt{2} \approx 1.41
  5. Divide to Get Answer: Since we need to round to the nearest hundredth, let's use a calculator to find the decimal value of 2\sqrt{2}.2≈1.41\sqrt{2} \approx 1.41Now divide 1.411.41 by 55 to get the final answer.1.415=0.282\frac{1.41}{5} = 0.282

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