Evaluate (6^2-(3) square root of 25)/( square root of 6^2+13)

$\frac{6^{2} - (3) \sqrt{25}}{\sqrt{6^{2} + 13}}$

Step 1

Simplify the numerator.

Raise $6$ to the power of $2$ .

$\frac{36 - 3 \sqrt{25}}{\sqrt{6^{2} + 13}}$

Rewrite $25$ as $5^{2}$ .

$\frac{36 - 3 \sqrt{5^{2}}}{\sqrt{6^{2} + 13}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{36 - 3 \cdot 5}{\sqrt{6^{2} + 13}}$

Multiply $- 3$ by $5$ .

$\frac{36 - 15}{\sqrt{6^{2} + 13}}$

Subtract $15$ from $36$ .

$\frac{21}{\sqrt{6^{2} + 13}}$

Step 2

Simplify the denominator.

Raise $6$ to the power of $2$ .

$\frac{21}{\sqrt{36 + 13}}$

Add $36$ and $13$ .

$\frac{21}{\sqrt{49}}$

Rewrite $49$ as $7^{2}$ .

$\frac{21}{\sqrt{7^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$\frac{21}{7}$

Step 3

Divide $21$ by $7$ .

$3$