Solve 5sqrt{48}+7sqrt{75}=

$$5 \sqrt { 48 } + 7 \sqrt { 75 } =$$

Evaluate

$$55\sqrt{3}\approx 95.262794416$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$5\times 4\sqrt{3}+7\sqrt{75}$$

Multiply 5 and 4 to get 20.

$$20\sqrt{3}+7\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$20\sqrt{3}+7\times 5\sqrt{3}$$

Multiply 7 and 5 to get 35.

$$20\sqrt{3}+35\sqrt{3}$$

Combine 20\sqrt{3} and 35\sqrt{3} to get 55\sqrt{3}.

$$55\sqrt{3}$$