Solve 18/sqrt{8}

$$\frac{ 18 }{ \sqrt{ 8 } }$$

Evaluate

$$\frac{9\sqrt{2}}{2}\approx 6.363961031$$

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}.

$$\frac{18}{2\sqrt{2}}$$

Rationalize the denominator of \frac{18}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{18\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{18\sqrt{2}}{2\times 2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{9\sqrt{2}}{2}$$