Solve 88/sqrt{8}sqrt{5}

$$\frac{ 88 }{ \sqrt{ 8 } } \sqrt{ 5 }$$

Evaluate

$$22\sqrt{10}\approx 69.570108524$$

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}.

$$\frac{88}{2\sqrt{2}}\sqrt{5}$$

Rationalize the denominator of \frac{88}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{88\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}\sqrt{5}$$

The square of \sqrt{2} is 2.

$$\frac{88\sqrt{2}}{2\times 2}\sqrt{5}$$

Cancel out 2\times 2 in both numerator and denominator.

$$22\sqrt{2}\sqrt{5}$$

To multiply \sqrt{2} and \sqrt{5}, multiply the numbers under the square root.

$$22\sqrt{10}$$