Gibson Owen
08/30/2024 · Middle School
Estimation a) Work out an estimate for the value of \( \sqrt{63.5 \times 101.7} \)
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( \sqrt(63.5*101.7) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt{63.5\times 101.7}\)
- step1: Multiply the numbers:
\(\sqrt{6457.95}\)
- step2: Rewrite the expression:
\(\sqrt{\frac{129159}{20}}\)
- step3: Use the properties of radicals:
\(\frac{\sqrt{129159}}{\sqrt{20}}\)
- step4: Simplify the expression:
\(\frac{3\sqrt{14351}}{2\sqrt{5}}\)
- step5: Multiply by the Conjugate:
\(\frac{3\sqrt{14351}\times \sqrt{5}}{2\sqrt{5}\times \sqrt{5}}\)
- step6: Multiply the numbers:
\(\frac{3\sqrt{71755}}{2\sqrt{5}\times \sqrt{5}}\)
- step7: Multiply the numbers:
\(\frac{3\sqrt{71755}}{10}\)
The estimated value for \( \sqrt{63.5 \times 101.7} \) is approximately 80.361371.
Quick Answer
The estimated value is about 80.361371.
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