Solve 4-sqrt{8}+sqrt{300}-sqrt{150}

$$4 - \sqrt { 8 } + \sqrt { 300 } - \sqrt { 150 }$$

Evaluate

$$10\sqrt{3}+4-2\sqrt{2}-5\sqrt{6}\approx 6.244632237$$

Solution Steps

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

$$4-2\sqrt{2}+\sqrt{300}-\sqrt{150}$$

Factor 300=10^{2}\times 3. Rewrite the square root of the product \sqrt{10^{2}\times 3} as the product of square roots \sqrt{10^{2}}\sqrt{3}. Take the square root of 10^{2}.

$$4-2\sqrt{2}+10\sqrt{3}-\sqrt{150}$$

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}.

$$4-2\sqrt{2}+10\sqrt{3}-5\sqrt{6}$$