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

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

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

Calculate 2 to the power of 2 and get 4.

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

Calculate 2 to the power of 3 and get 8.

$$\sqrt{4+8}$$

Add 4 and 8 to get 12.

$$\sqrt{12}$$

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}.

$$2\sqrt{3}$$