Simplify (8 square root of 5)/(2 square root of 36)

$\frac{8 \sqrt{5}}{2 \sqrt{36}}$

Step 1

Cancel the common factor of $8$ and $2$ .

Factor $2$ out of $8 \sqrt{5}$ .

$\frac{2 (4 \sqrt{5})}{2 \sqrt{36}}$

Cancel the common factors.

Factor $2$ out of $2 \sqrt{36}$ .

$\frac{2 (4 \sqrt{5})}{2 (\sqrt{36})}$

Cancel the common factor.

$\frac{2 (4 \sqrt{5})}{2 \sqrt{36}}$

Rewrite the expression.

$\frac{4 \sqrt{5}}{\sqrt{36}}$

Step 2

Simplify the denominator.

Rewrite $36$ as $6^{2}$ .

$\frac{4 \sqrt{5}}{\sqrt{6^{2}}}$

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

$\frac{4 \sqrt{5}}{6}$

Step 3

Cancel the common factor of $4$ and $6$ .

Factor $2$ out of $4 \sqrt{5}$ .

$\frac{2 (2 \sqrt{5})}{6}$

Cancel the common factors.

Factor $2$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.49071198 \dots$