Solve sqrt{79,67/2}

$$\sqrt { \frac { 79,67 } { 2 } }$$

Evaluate

$$\frac{\sqrt{15934}}{20}\approx 6.311497445$$

Solution Steps

Expand \frac{79,67}{2} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{7967}{200}}$$

Rewrite the square root of the division \sqrt{\frac{7967}{200}} as the division of square roots \frac{\sqrt{7967}}{\sqrt{200}}.

$$\frac{\sqrt{7967}}{\sqrt{200}}$$

Factor 200=10^{2}\times 2. Rewrite the square root of the product \sqrt{10^{2}\times 2} as the product of square roots \sqrt{10^{2}}\sqrt{2}. Take the square root of 10^{2}.

$$\frac{\sqrt{7967}}{10\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{7967}}{10\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\sqrt{7967}\sqrt{2}}{10\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\sqrt{7967}\sqrt{2}}{10\times 2}$$

To multiply \sqrt{7967} and \sqrt{2}, multiply the numbers under the square root.

$$\frac{\sqrt{15934}}{10\times 2}$$

Multiply 10 and 2 to get 20.

$$\frac{\sqrt{15934}}{20}$$