Solve sqrt{54}-2sqrt{18}

$$\sqrt { 54 } - 2 \sqrt { 18 }$$

Evaluate

$$3\left(\sqrt{6}-2\sqrt{2}\right)\approx -1.136812146$$

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}.

$$3\sqrt{6}-2\sqrt{18}$$

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}.

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

Multiply -2 and 3 to get -6.

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