Solve sqrt{54}-2sqrt{8}

$$\sqrt { 54 } - 2 \sqrt { 8 }$$

Evaluate

$$3\sqrt{6}-4\sqrt{2}\approx 1.691614979$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$3\sqrt{6}-2\sqrt{8}$$

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}.

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

Multiply -2 and 2 to get -4.

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