Solve 5sqrt{12}-(3sqrt{8}+2sqrt{27})=

$$5 \sqrt { 12 } - ( 3 \sqrt { 8 } + 2 \sqrt { 27 } ) =$$

Evaluate

$$2\sqrt{2}\left(\sqrt{6}-3\right)\approx -1.557078144$$

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}.

$$5\times 2\sqrt{3}-\left(3\sqrt{8}+2\sqrt{27}\right)$$

Multiply 5 and 2 to get 10.

$$10\sqrt{3}-\left(3\sqrt{8}+2\sqrt{27}\right)$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$10\sqrt{3}-\left(3\times 2\sqrt{2}+2\sqrt{27}\right)$$

Multiply 3 and 2 to get 6.

$$10\sqrt{3}-\left(6\sqrt{2}+2\sqrt{27}\right)$$

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}.

$$10\sqrt{3}-\left(6\sqrt{2}+2\times 3\sqrt{3}\right)$$

Multiply 2 and 3 to get 6.

$$10\sqrt{3}-\left(6\sqrt{2}+6\sqrt{3}\right)$$

To find the opposite of 6\sqrt{2}+6\sqrt{3}, find the opposite of each term.

$$10\sqrt{3}-6\sqrt{2}-6\sqrt{3}$$

Combine 10\sqrt{3} and -6\sqrt{3} to get 4\sqrt{3}.

$$4\sqrt{3}-6\sqrt{2}$$