Solve sqrt{48}+5sqrt{12}=

$$\sqrt { 48 } + 5 \sqrt { 12 } =$$

Evaluate

$$14\sqrt{3}\approx 24.248711306$$

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}.

$$4\sqrt{3}+5\sqrt{12}$$

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}.

$$4\sqrt{3}+5\times 2\sqrt{3}$$

Multiply 5 and 2 to get 10.

$$4\sqrt{3}+10\sqrt{3}$$

Combine 4\sqrt{3} and 10\sqrt{3} to get 14\sqrt{3}.

$$14\sqrt{3}$$