Solve 10sqrt{150}+sqrt{150}

$$10 \sqrt { 150 } + \sqrt { 150 }$$

Evaluate

$$55\sqrt{6}\approx 134.721935853$$

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}.

$$10\times 5\sqrt{6}+\sqrt{150}$$

Multiply 10 and 5 to get 50.

$$50\sqrt{6}+\sqrt{150}$$

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}.

$$50\sqrt{6}+5\sqrt{6}$$

Combine 50\sqrt{6} and 5\sqrt{6} to get 55\sqrt{6}.

$$55\sqrt{6}$$