Question

1. simplify the expression.

$6\sqrt{\frac{25}{36}} - \sqrt{49}$
select the correct choice below and fill in any answer boxes in your choice.
\\(\bigcirc\\) a.
$6\sqrt{\frac{25}{36}} - \sqrt{49} = \square$
(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 \(\sqrt{\frac{25}{36}}\) and \(\sqrt{49}\). We know that \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) (for \(a\geq0,b > 0\)) and \(\sqrt{a^2}=a\) (for \(a\geq0\)). So, \(\sqrt{\frac{25}{36}}=\frac{\sqrt{25}}{\sqrt{36}}=\frac{5}{6}\) and \(\sqrt{49} = 7\) since \(7^2=49\).

Step2: Substitute and calculate

Now substitute these values back into the original expression \(6\sqrt{\frac{25}{36}}-\sqrt{49}\). We have \(6\times\frac{5}{6}-7\). The \(6\) in the numerator and denominator of the first term cancels out, so \(6\times\frac{5}{6}=5\). Then we subtract \(7\) from \(5\): \(5 - 7=- 2\).

Answer:

\(-2\)