Simplify the Radical Expression (20 square root of 270)/(4 square root of 3)

$\frac{20 \sqrt{270}}{4 \sqrt{3}}$

Step 1

Cancel the common factor of $20$ and $4$ .

Factor $4$ out of $20 \sqrt{270}$ .

$\frac{4 (5 \sqrt{270})}{4 \sqrt{3}}$

Cancel the common factors.

Factor $4$ out of $4 \sqrt{3}$ .

$\frac{4 (5 \sqrt{270})}{4 (\sqrt{3})}$

Cancel the common factor.

$\frac{4 (5 \sqrt{270})}{4 \sqrt{3}}$

Rewrite the expression.

$\frac{5 \sqrt{270}}{\sqrt{3}}$

Step 2

Combine $\sqrt{270}$ and $\sqrt{3}$ into a single radical.

$5 \sqrt{\frac{270}{3}}$

Step 3

Divide $270$ by $3$ .

$5 \sqrt{90}$

Step 4

Rewrite $90$ as $3^{2} \cdot 10$ .

Factor $9$ out of $90$ .

$5 \sqrt{9 (10)}$

Rewrite $9$ as $3^{2}$ .

$5 \sqrt{3^{2} \cdot 10}$

Step 5

Pull terms out from under the radical.

$5 (| 3 | \sqrt{10})$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $3$ is $3$ .

$5 (3 \sqrt{10})$

Step 7

Multiply $3$ by $5$ .

$15 \sqrt{10}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$15 \sqrt{10}$

Decimal Form:

$47.43416490 \dots$