Solve 2^3sqrt{3*+6}+2

$${ 2 }^{ 3 } \sqrt{ 3 \times +6 } +2$$

Evaluate

$$24\sqrt{2}+2\approx 35.941125497$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$8\sqrt{3\times 6}+2$$

Multiply 3 and 6 to get 18.

$$8\sqrt{18}+2$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$8\times 3\sqrt{2}+2$$

Multiply 8 and 3 to get 24.

$$24\sqrt{2}+2$$

Factor

$$2 {(12 \sqrt{2} + 1)} = 35.941125497$$