Solve 5sqrt{12}+3sqrt{75}

$$5 \sqrt { 12 } + 3 \sqrt { 75 }$$

Evaluate

$$25\sqrt{3}\approx 43.301270189$$

Solution Steps

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$5\times 2\sqrt{3}+3\sqrt{75}$$

Multiply 5 and 2 to get 10.

$$10\sqrt{3}+3\sqrt{75}$$

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}.

$$10\sqrt{3}+3\times 5\sqrt{3}$$

Multiply 3 and 5 to get 15.

$$10\sqrt{3}+15\sqrt{3}$$

Combine 10\sqrt{3} and 15\sqrt{3} to get 25\sqrt{3}.

$$25\sqrt{3}$$