Solve 4sqrt{8}-sqrt{18}=

$$4 \sqrt { 8 } - \sqrt { 18 } =$$

Evaluate

$$5\sqrt{2}\approx 7.071067812$$

Solution Steps

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}.

$$4\times 2\sqrt{2}-\sqrt{18}$$

Multiply 4 and 2 to get 8.

$$8\sqrt{2}-\sqrt{18}$$

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}.

$$8\sqrt{2}-3\sqrt{2}$$

Combine 8\sqrt{2} and -3\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}$$