Question

Calculate the value $\sqrt{\frac{256}{6400}}\times\sqrt{\frac{25}{7056}}$

• A. 16/80
• B. 5/80
• C. 1/84
• D. 80/5

Answer 1

Answer:

C. 1/84

The value is $\frac{1}{84}$.

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1. Simplify the first square root

$\sqrt{\frac{256}{6400}} = \frac{\sqrt{256}}{\sqrt{6400}}$

• $\sqrt{256} = 16$

• $\sqrt{6400} = 80$

This gives:
$\frac{16}{80} = \frac{1}{5}$

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2. Simplify the second square root

$\sqrt{\frac{25}{7056}} = \frac{\sqrt{25}}{\sqrt{7056}}$

• $\sqrt{25} = 5$

• $\sqrt{7056} = 84$ (since $84 \times 84 = 7056$)

This gives:
$\frac{5}{84}$

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3. Multiply the two fractions together

$\frac{1}{5} \times \frac{5}{84}$

Cancel out the common factor of 5 from the numerator and denominator:
$\frac{1}{84}$