Solve {l}{9sqrt{3}-5sqrt{48}}{+7sqrt{12}}

$$\left. \begin{array} { l } { 9 \sqrt { 3 } - 5 \sqrt { 48 } } \\ { + 7 \sqrt { 12 } } \end{array} \right.$$

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

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}.

$$9\sqrt{3}-5\times 4\sqrt{3}+7\sqrt{12}$$

Multiply -5 and 4 to get -20.

$$9\sqrt{3}-20\sqrt{3}+7\sqrt{12}$$

Combine 9\sqrt{3} and -20\sqrt{3} to get -11\sqrt{3}.

$$-11\sqrt{3}+7\sqrt{12}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$-11\sqrt{3}+7\times 2\sqrt{3}$$

Multiply 7 and 2 to get 14.

$$-11\sqrt{3}+14\sqrt{3}$$

Combine -11\sqrt{3} and 14\sqrt{3} to get 3\sqrt{3}.

$$3\sqrt{3}$$