Solve (5sqrt{48}-6sqrt{27})divsqrt{3}

$$( 5 \sqrt { 48 } - 6 \sqrt { 27 } ) \div \sqrt { 3 }$$

Evaluate

$$2$$

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}.

$$\frac{5\times 4\sqrt{3}-6\sqrt{27}}{\sqrt{3}}$$

Multiply 5 and 4 to get 20.

$$\frac{20\sqrt{3}-6\sqrt{27}}{\sqrt{3}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\frac{20\sqrt{3}-6\times 3\sqrt{3}}{\sqrt{3}}$$

Multiply -6 and 3 to get -18.

$$\frac{20\sqrt{3}-18\sqrt{3}}{\sqrt{3}}$$

Combine 20\sqrt{3} and -18\sqrt{3} to get 2\sqrt{3}.

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

Rationalize the denominator of \frac{2\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

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

The square of \sqrt{3} is 3.

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

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

$$\frac{2\times 3}{3}$$

Multiply 2 and 3 to get 6.

$$\frac{6}{3}$$

Divide 6 by 3 to get 2.

$$2$$

Factor

$$2$$