Simplify the Radical Expression ( square root of 252)/3

$\frac{\sqrt{252}}{3}$

Step 1

Simplify the numerator.

Rewrite $252$ as $6^{2} \cdot 7$ .

Factor $36$ out of $252$ .

$\frac{\sqrt{36 (7)}}{3}$

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

$\frac{\sqrt{6^{2} \cdot 7}}{3}$

Pull terms out from under the radical.

$\frac{| 6 | \sqrt{7}}{3}$

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$\frac{6 \sqrt{7}}{3}$

Step 2

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6 \sqrt{7}$ .

$\frac{3 (2 \sqrt{7})}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{3 (2 \sqrt{7})}{3 (1)}$

Cancel the common factor.

$\frac{3 (2 \sqrt{7})}{3 \cdot 1}$

Rewrite the expression.

$\frac{2 \sqrt{7}}{1}$

Divide $2 \sqrt{7}$ by $1$ .

$2 \sqrt{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{7}$

Decimal Form:

$5.29150262 \dots$