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 final value of the expression is $\frac{1}{84}$.

1. Simplify the First Square Root

• $\sqrt{256} = 16$

• $\sqrt{6400} = 80$

• $\sqrt{\frac{256}{6400}} = \frac{16}{80} = \frac{1}{5}$

2. Simplify the Second Square Root

• $\sqrt{25} = 5$

• $\sqrt{7056} = 84$

• $\sqrt{\frac{25}{7056}} = \frac{5}{84}$

3. Multiply the Simplified Fractions

Now, multiply the two results together:
$\frac{1}{5} \times \frac{5}{84} = \frac{1 \times \not5}{\not5 \times 84} = \frac{1}{84}$