Solve sqrt{150}+7sqrt{24}

$$\sqrt{ 150 } +7 \sqrt{ 24 }$$

Evaluate

$$19\sqrt{6}\approx 46.540305113$$

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}.

$$5\sqrt{6}+7\sqrt{24}$$

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}.

$$5\sqrt{6}+7\times 2\sqrt{6}$$

Multiply 7 and 2 to get 14.

$$5\sqrt{6}+14\sqrt{6}$$

Combine 5\sqrt{6} and 14\sqrt{6} to get 19\sqrt{6}.

$$19\sqrt{6}$$