Solve (sqrt{48}+sqrt{27})divsqrt{3}-2

$$( \sqrt { 48 } + \sqrt { 27 } ) \div \sqrt { 3 } - 2$$

Evaluate

$$5$$

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}.

$$\frac{4\sqrt{3}+\sqrt{27}}{\sqrt{3}}-2$$

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}.

$$\frac{4\sqrt{3}+3\sqrt{3}}{\sqrt{3}}-2$$

Combine 4\sqrt{3} and 3\sqrt{3} to get 7\sqrt{3}.

$$\frac{7\sqrt{3}}{\sqrt{3}}-2$$

Rationalize the denominator of \frac{7\sqrt{3}}{\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{7\sqrt{3}\sqrt{3}}{\left(\sqrt{3}\right)^{2}}-2$$

The square of \sqrt{3} is 3.

$$\frac{7\sqrt{3}\sqrt{3}}{3}-2$$

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

$$\frac{7\times 3}{3}-2$$

Multiply 7 and 3 to get 21.

$$\frac{21}{3}-2$$

Divide 21 by 3 to get 7.

$$7-2$$

Subtract 2 from 7 to get 5.

$$5$$

Factor

$$5$$