Solve frac{sqrt{3^2-1}}{3-1}

$$\frac { \sqrt { 3 ^ { 2 } - 1 } } { 3 - 1 }$$

Evaluate

$$\sqrt{2}\approx 1.414213562$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{\sqrt{9-1}}{3-1}$$

Subtract 1 from 9 to get 8.

$$\frac{\sqrt{8}}{3-1}$$

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}.

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

Subtract 1 from 3 to get 2.

$$\frac{2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$\sqrt{2}$$