Solve sqrt{150}-sqrt{54}

$$\sqrt { 150 } - \sqrt { 54 }$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Factor 150=5^{2}\times 6. Rewrite the square root of the product \sqrt{5^{2}\times 6} as the product of square roots \sqrt{5^{2}}\sqrt{6}. Take the square root of 5^{2}.

$$5\sqrt{6}-\sqrt{54}$$

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}.

$$5\sqrt{6}-3\sqrt{6}$$

Combine 5\sqrt{6} and -3\sqrt{6} to get 2\sqrt{6}.

$$2\sqrt{6}$$