Question

1. simplify the expression.

$8\sqrt{\frac{49}{64}} - \sqrt{100}$
select the correct choice below and fill in any answer boxes in your choice.
\\(\bigcirc\\) a.
$8\sqrt{\frac{49}{64}} - \sqrt{100} = \square$
(simplify your answer. type an exact answer, using radicals as needed.)
\\(\bigcirc\\) b. the answer is not a real number.

Explanation:

Step1: Simplify the square roots

First, simplify $\sqrt{\frac{49}{64}}$ and $\sqrt{100}$. We know that $\sqrt{\frac{49}{64}}=\frac{\sqrt{49}}{\sqrt{64}}=\frac{7}{8}$ because $7^2 = 49$ and $8^2 = 64$. Also, $\sqrt{100}=10$ since $10^2 = 100$.

Step2: Substitute and calculate

Now substitute these values back into the original expression: $8\times\frac{7}{8}-10$. The $8$ in the numerator and denominator of the first term cancels out, leaving $7 - 10$.

Step3: Final subtraction

Calculate $7 - 10=-3$.

Answer:

A. $8\sqrt{\frac{49}{64}} - \sqrt{100}=\boxed{-3}$