Solve frac{3sqrt{48}}{sqrt{3}}=

$$\frac { 3 \sqrt { 48 } } { \sqrt { 3 } } =$$

Evaluate

$$12$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\frac{3\times 4\sqrt{3}}{\sqrt{3}}$$

Multiply 3 and 4 to get 12.

$$\frac{12\sqrt{3}}{\sqrt{3}}$$

Rationalize the denominator of \frac{12\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{12\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{12\sqrt{3}\sqrt{3}}{3}$$

Multiply \sqrt{3} and \sqrt{3} to get 3.

$$\frac{12\times 3}{3}$$

Multiply 12 and 3 to get 36.

$$\frac{36}{3}$$

Divide 36 by 3 to get 12.

$$12$$

Factor

$$2^{2}\times 3$$