Solve 5sqrt{36}-7sqrt{8}+sqrt{18}=

$$5 \sqrt { 36 } - 7 \sqrt { 8 } + \sqrt { 18 } =$$

Evaluate

$$30-11\sqrt{2}\approx 14.443650814$$

Solution Steps

Calculate the square root of 36 and get 6.

$$5\times 6-7\sqrt{8}+\sqrt{18}$$

Multiply 5 and 6 to get 30.

$$30-7\sqrt{8}+\sqrt{18}$$

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}.

$$30-7\times 2\sqrt{2}+\sqrt{18}$$

Multiply -7 and 2 to get -14.

$$30-14\sqrt{2}+\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$30-14\sqrt{2}+3\sqrt{2}$$

Combine -14\sqrt{2} and 3\sqrt{2} to get -11\sqrt{2}.

$$30-11\sqrt{2}$$