Solve sqrt{750}-sqrt{24}+sqrt{54}+sqrt{6}

$$\sqrt { 750 } - \sqrt { 24 } + \sqrt { 54 } + \sqrt { 6 }$$

Evaluate

$$2\sqrt{6}+5\sqrt{30}\approx 32.285107361$$

Solution Steps

Factor 750=5^{2}\times 30. Rewrite the square root of the product \sqrt{5^{2}\times 30} as the product of square roots \sqrt{5^{2}}\sqrt{30}. Take the square root of 5^{2}.

$$5\sqrt{30}-\sqrt{24}+\sqrt{54}+\sqrt{6}$$

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}.

$$5\sqrt{30}-2\sqrt{6}+\sqrt{54}+\sqrt{6}$$

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}.

$$5\sqrt{30}-2\sqrt{6}+3\sqrt{6}+\sqrt{6}$$

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

$$5\sqrt{30}+\sqrt{6}+\sqrt{6}$$

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

$$5\sqrt{30}+2\sqrt{6}$$