Solve {l}{5sqrt{12}-2sqrt{7}}{+3sqrt{3}}

$$\left. \begin{array} { l } { 5 \sqrt { 12 } - 2 \sqrt { 7 } } \\ { + 3 \sqrt { 3 } } \end{array} \right.$$

Evaluate

$$13\sqrt{3}-2\sqrt{7}\approx 17.225157876$$

Solution Steps

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}.

$$5\times 2\sqrt{3}-2\sqrt{7}+3\sqrt{3}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{3}-2\sqrt{7}+3\sqrt{3}$$

Combine 10\sqrt{3} and 3\sqrt{3} to get 13\sqrt{3}.

$$13\sqrt{3}-2\sqrt{7}$$