Solve sqrt{2*163/97864}

$$\sqrt{ \frac{ 2 \times 163 }{ 97864 } }$$

Evaluate

$$\frac{\sqrt{1993979}}{24466}\approx 0.057716145$$

Solution Steps

Multiply 2 and 163 to get 326.

$$\sqrt{\frac{326}{97864}}$$

Reduce the fraction \frac{326}{97864} to lowest terms by extracting and canceling out 2.

$$\sqrt{\frac{163}{48932}}$$

Rewrite the square root of the division \sqrt{\frac{163}{48932}} as the division of square roots \frac{\sqrt{163}}{\sqrt{48932}}.

$$\frac{\sqrt{163}}{\sqrt{48932}}$$

Factor 48932=2^{2}\times 12233. Rewrite the square root of the product \sqrt{2^{2}\times 12233} as the product of square roots \sqrt{2^{2}}\sqrt{12233}. Take the square root of 2^{2}.

$$\frac{\sqrt{163}}{2\sqrt{12233}}$$

Rationalize the denominator of \frac{\sqrt{163}}{2\sqrt{12233}} by multiplying numerator and denominator by \sqrt{12233}.

$$\frac{\sqrt{163}\sqrt{12233}}{2\left(\sqrt{12233}\right)^{2}}$$

The square of \sqrt{12233} is 12233.

$$\frac{\sqrt{163}\sqrt{12233}}{2\times 12233}$$

To multiply \sqrt{163} and \sqrt{12233}, multiply the numbers under the square root.

$$\frac{\sqrt{1993979}}{2\times 12233}$$

Multiply 2 and 12233 to get 24466.

$$\frac{\sqrt{1993979}}{24466}$$