Solve frac{sqrt{78div16}}{}

$$\frac{ \sqrt{ 78 \div 16 } }{ }$$

Evaluate

$$\frac{\sqrt{78}}{4}\approx 2.207940217$$

Solution Steps

Reduce the fraction \frac{78}{16} to lowest terms by extracting and canceling out 2.

$$\frac{\sqrt{\frac{39}{8}}}{1}$$

Rewrite the square root of the division \sqrt{\frac{39}{8}} as the division of square roots \frac{\sqrt{39}}{\sqrt{8}}.

$$\frac{\frac{\sqrt{39}}{\sqrt{8}}}{1}$$

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}.

$$\frac{\frac{\sqrt{39}}{2\sqrt{2}}}{1}$$

Rationalize the denominator of \frac{\sqrt{39}}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\frac{\sqrt{39}\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}}{1}$$

The square of \sqrt{2} is 2.

$$\frac{\frac{\sqrt{39}\sqrt{2}}{2\times 2}}{1}$$

To multiply \sqrt{39} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\frac{\sqrt{78}}{2\times 2}}{1}$$

Multiply 2 and 2 to get 4.

$$\frac{\frac{\sqrt{78}}{4}}{1}$$

Anything divided by one gives itself.

$$\frac{\sqrt{78}}{4}$$