Simplify the Radical Expression 12 square root of 25/64

$12 \sqrt{\frac{25}{64}}$

Step 1

Rewrite $\sqrt{\frac{25}{64}}$ as $\frac{\sqrt{25}}{\sqrt{64}}$ .

$12 \frac{\sqrt{25}}{\sqrt{64}}$

Step 2

Simplify the numerator.

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

$12 \frac{\sqrt{5^{2}}}{\sqrt{64}}$

Pull terms out from under the radical.

$12 \frac{| 5 |}{\sqrt{64}}$

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$12 \frac{5}{\sqrt{64}}$

Step 3

Simplify the denominator.

Rewrite $64$ as $8^{2}$ .

$12 \frac{5}{\sqrt{8^{2}}}$

Pull terms out from under the radical.

$12 \frac{5}{| 8 |}$

The absolute value is the distance between a number and zero. The distance between $0$ and $8$ is $8$ .

$12 (\frac{5}{8})$

Step 4

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$4 (3) \frac{5}{8}$

Factor $4$ out of $8$ .

$4 \cdot 3 \frac{5}{4 \cdot 2}$

Cancel the common factor.

$4 \cdot 3 \frac{5}{4 \cdot 2}$

Rewrite the expression.

$3 (\frac{5}{2})$

Step 5

Combine $3$ and $\frac{5}{2}$ .

$\frac{3 \cdot 5}{2}$

Step 6

Multiply $3$ by $5$ .

$\frac{15}{2}$