Solve sqrt{8}+(sqrt{2}-1)+(1/2)^0

$$\sqrt { 8 } + ( \sqrt { 2 } - 1 ) + ( \frac { 1 } { 2 } ) ^ { 0 }$$

Evaluate

$$3\sqrt{2}\approx 4.242640687$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$2\sqrt{2}+\sqrt{2}-1+\left(\frac{1}{2}\right)^{0}$$

Combine 2\sqrt{2} and \sqrt{2} to get 3\sqrt{2}.

$$3\sqrt{2}-1+\left(\frac{1}{2}\right)^{0}$$

Calculate \frac{1}{2} to the power of 0 and get 1.

$$3\sqrt{2}-1+1$$

Add -1 and 1 to get 0.

$$3\sqrt{2}$$