Solve sqrt{216}-4sqrt{24}+sqrt{600}-sqrt{150}

$$\sqrt { 216 } - 4 \sqrt { 24 } + \sqrt { 600 } - \sqrt { 150 }$$

Evaluate

$$3\sqrt{6}\approx 7.348469228$$

Solution Steps

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$6\sqrt{6}-4\sqrt{24}+\sqrt{600}-\sqrt{150}$$

Factor 24=2^{2}\times 6. Rewrite the square root of the product \sqrt{2^{2}\times 6} as the product of square roots \sqrt{2^{2}}\sqrt{6}. Take the square root of 2^{2}.

$$6\sqrt{6}-4\times 2\sqrt{6}+\sqrt{600}-\sqrt{150}$$

Multiply -4 and 2 to get -8.

$$6\sqrt{6}-8\sqrt{6}+\sqrt{600}-\sqrt{150}$$

Combine 6\sqrt{6} and -8\sqrt{6} to get -2\sqrt{6}.

$$-2\sqrt{6}+\sqrt{600}-\sqrt{150}$$

Factor 600=10^{2}\times 6. Rewrite the square root of the product \sqrt{10^{2}\times 6} as the product of square roots \sqrt{10^{2}}\sqrt{6}. Take the square root of 10^{2}.

$$-2\sqrt{6}+10\sqrt{6}-\sqrt{150}$$

Combine -2\sqrt{6} and 10\sqrt{6} to get 8\sqrt{6}.

$$8\sqrt{6}-\sqrt{150}$$

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}.

$$8\sqrt{6}-5\sqrt{6}$$

Combine 8\sqrt{6} and -5\sqrt{6} to get 3\sqrt{6}.

$$3\sqrt{6}$$