Solve sqrt{0.79/0.8}

$$\sqrt{ \frac{ 0.79 }{ 0.8 } }$$

Evaluate

$$\frac{\sqrt{395}}{20}\approx 0.993730346$$

Solution Steps

Expand \frac{0.79}{0.8} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{79}{80}}$$

Rewrite the square root of the division \sqrt{\frac{79}{80}} as the division of square roots \frac{\sqrt{79}}{\sqrt{80}}.

$$\frac{\sqrt{79}}{\sqrt{80}}$$

Factor 80=4^{2}\times 5. Rewrite the square root of the product \sqrt{4^{2}\times 5} as the product of square roots \sqrt{4^{2}}\sqrt{5}. Take the square root of 4^{2}.

$$\frac{\sqrt{79}}{4\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{79}}{4\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{79}\sqrt{5}}{4\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{79}\sqrt{5}}{4\times 5}$$

To multiply \sqrt{79} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{395}}{4\times 5}$$

Multiply 4 and 5 to get 20.

$$\frac{\sqrt{395}}{20}$$