Simplify (-4 square root of 3)/(- square root of 48)

$\frac{- 4 \sqrt{3}}{- \sqrt{48}}$

Step 1

Combine $\sqrt{3}$ and $\sqrt{48}$ into a single radical.

$\frac{- 4 \sqrt{\frac{3}{48}}}{- 1}$

Step 2

Cancel the common factor of $3$ and $48$ .

Factor $3$ out of $3$ .

$\frac{- 4 \sqrt{\frac{3 (1)}{48}}}{- 1}$

Cancel the common factors.

Factor $3$ out of $48$ .

$\frac{- 4 \sqrt{\frac{3 \cdot 1}{3 \cdot 16}}}{- 1}$

Cancel the common factor.

$\frac{- 4 \sqrt{\frac{3 \cdot 1}{3 \cdot 16}}}{- 1}$

Rewrite the expression.

$\frac{- 4 \sqrt{\frac{1}{16}}}{- 1}$

Step 3

Simplify the expression.

Move the negative one from the denominator of $\frac{- 4 \sqrt{\frac{1}{16}}}{- 1}$ .

$- 1 \cdot (- 4 \sqrt{\frac{1}{16}})$

Rewrite $- 1 \cdot (- 4 \sqrt{\frac{1}{16}})$ as $- (- 4 \sqrt{\frac{1}{16}})$ .

$- (- 4 \sqrt{\frac{1}{16}})$

Step 4

Rewrite $\sqrt{\frac{1}{16}}$ as $\frac{\sqrt{1}}{\sqrt{16}}$ .

$- (- 4 \frac{\sqrt{1}}{\sqrt{16}})$

Step 5

Any root of $1$ is $1$ .

$- (- 4 \frac{1}{\sqrt{16}})$

Step 6

Simplify the denominator.

Rewrite $16$ as $4^{2}$ .

$- (- 4 \frac{1}{\sqrt{4^{2}}})$

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

$- (- 4 (\frac{1}{4}))$

Step 7

Reduce the expression by cancelling the common factors.

Cancel the common factor of $4$ .

Factor $4$ out of $- 4$ .

$- (4 (- 1) \frac{1}{4})$

Cancel the common factor.

$- (4 \cdot - 1 \frac{1}{4})$

Rewrite the expression.

$- - 1$

Multiply $- 1$ by $- 1$ .

$1$