Solve 3sqrt{40}+2sqrt{54}-sqrt{96}-sqrt{150}

$$3 \sqrt{ 40 } +2 \sqrt{ 54 } - \sqrt{ 96 } - \sqrt{ 150 }$$

Evaluate

$$6\sqrt{10}-3\sqrt{6}\approx 11.625196733$$

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$3\times 2\sqrt{10}+2\sqrt{54}-\sqrt{96}-\sqrt{150}$$

Multiply 3 and 2 to get 6.

$$6\sqrt{10}+2\sqrt{54}-\sqrt{96}-\sqrt{150}$$

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}.

$$6\sqrt{10}+2\times 3\sqrt{6}-\sqrt{96}-\sqrt{150}$$

Multiply 2 and 3 to get 6.

$$6\sqrt{10}+6\sqrt{6}-\sqrt{96}-\sqrt{150}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$6\sqrt{10}+6\sqrt{6}-4\sqrt{6}-\sqrt{150}$$

Combine 6\sqrt{6} and -4\sqrt{6} to get 2\sqrt{6}.

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

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}.

$$6\sqrt{10}+2\sqrt{6}-5\sqrt{6}$$

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

$$6\sqrt{10}-3\sqrt{6}$$