Simplify ( square root of 84)/(2 square root of 3)

$\frac{\sqrt{84}}{2 \sqrt{3}}$

Step 1

Combine $\sqrt{84}$ and $\sqrt{3}$ into a single radical.

$\frac{\sqrt{\frac{84}{3}}}{2}$

Step 2

Cancel the common factor of $84$ and $3$ .

Factor $3$ out of $84$ .

$\frac{\sqrt{\frac{3 \cdot 28}{3}}}{2}$

Cancel the common factors.

Factor $3$ out of $3$ .

$\frac{\sqrt{\frac{3 \cdot 28}{3 (1)}}}{2}$

Cancel the common factor.

$\frac{\sqrt{\frac{3 \cdot 28}{3 \cdot 1}}}{2}$

Rewrite the expression.

$\frac{\sqrt{\frac{28}{1}}}{2}$

Divide $28$ by $1$ .

$\frac{\sqrt{28}}{2}$

Step 3

Simplify the numerator.

Rewrite $28$ as $2^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$\frac{\sqrt{4 (7)}}{2}$

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

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

Pull terms out from under the radical.

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

Step 4

Cancel the common factor of $2$ .

Cancel the common factor.

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

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

$\sqrt{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\sqrt{7}$

Decimal Form:

$2.64575131 \dots$