Solve sqrt{32}+sqrt{48}divsqrt{8}+sqrt{12}

$$\sqrt{ 32 } + \sqrt{ 48 } \div \sqrt{ 8 } + \sqrt{ 12 }$$

Evaluate

$$\sqrt{6}+2\sqrt{3}+4\sqrt{2}\approx 11.570445607$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

$$4\sqrt{2}+\frac{\sqrt{48}}{\sqrt{8}}+\sqrt{12}$$

Rewrite the division of square roots \frac{\sqrt{48}}{\sqrt{8}} as the square root of the division \sqrt{\frac{48}{8}} and perform the division.

$$4\sqrt{2}+\sqrt{6}+\sqrt{12}$$

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}.

$$4\sqrt{2}+\sqrt{6}+2\sqrt{3}$$