Simplify the Radical Expression (-45 square root of 156)/(9 square root of 3)

$\frac{- 45 \sqrt{156}}{9 \sqrt{3}}$

Step 1

Cancel the common factor of $- 45$ and $9$ .

Factor $9$ out of $- 45 \sqrt{156}$ .

$\frac{9 (- 5 \sqrt{156})}{9 \sqrt{3}}$

Cancel the common factors.

Factor $9$ out of $9 \sqrt{3}$ .

$\frac{9 (- 5 \sqrt{156})}{9 (\sqrt{3})}$

Cancel the common factor.

$\frac{9 (- 5 \sqrt{156})}{9 \sqrt{3}}$

Rewrite the expression.

$\frac{- 5 \sqrt{156}}{\sqrt{3}}$

Step 2

Combine $\sqrt{156}$ and $\sqrt{3}$ into a single radical.

$- 5 \sqrt{\frac{156}{3}}$

Step 3

Divide $156$ by $3$ .

$- 5 \sqrt{52}$

Step 4

Rewrite $52$ as $2^{2} \cdot 13$ .

Factor $4$ out of $52$ .

$- 5 \sqrt{4 (13)}$

Rewrite $4$ as $2^{2}$ .

$- 5 \sqrt{2^{2} \cdot 13}$

Step 5

Pull terms out from under the radical.

$- 5 (| 2 | \sqrt{13})$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$- 5 (2 \sqrt{13})$

Step 7

Multiply $2$ by $- 5$ .

$- 10 \sqrt{13}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$- 10 \sqrt{13}$

Decimal Form:

$- 36.05551275 \dots$