Solve sqrt{150}-3sqrt{147}-sqrt{54}+sqrt{192}

$$\sqrt { 150 } - 3 \sqrt { 147 } - \sqrt { 54 } + \sqrt { 192 }$$

Evaluate

$$2\sqrt{6}-13\sqrt{3}\approx -17.617681013$$

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}.

$$5\sqrt{6}-3\sqrt{147}-\sqrt{54}+\sqrt{192}$$

Factor 147=7^{2}\times 3. Rewrite the square root of the product \sqrt{7^{2}\times 3} as the product of square roots \sqrt{7^{2}}\sqrt{3}. Take the square root of 7^{2}.

$$5\sqrt{6}-3\times 7\sqrt{3}-\sqrt{54}+\sqrt{192}$$

Multiply -3 and 7 to get -21.

$$5\sqrt{6}-21\sqrt{3}-\sqrt{54}+\sqrt{192}$$

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}.

$$5\sqrt{6}-21\sqrt{3}-3\sqrt{6}+\sqrt{192}$$

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

$$2\sqrt{6}-21\sqrt{3}+\sqrt{192}$$

Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.

$$2\sqrt{6}-21\sqrt{3}+8\sqrt{3}$$

Combine -21\sqrt{3} and 8\sqrt{3} to get -13\sqrt{3}.

$$2\sqrt{6}-13\sqrt{3}$$