sqrt{49/108}-এর সমাধান করুন

$$\sqrt{ \frac{ 49 }{ 108 } }$$

Evaluate

$$\frac{7\sqrt{3}}{18}\approx 0.673575314$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{49}{108}} as the division of square roots \frac{\sqrt{49}}{\sqrt{108}}.

$$\frac{\sqrt{49}}{\sqrt{108}}$$

Calculate the square root of 49 and get 7.

$$\frac{7}{\sqrt{108}}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$\frac{7}{6\sqrt{3}}$$

Rationalize the denominator of \frac{7}{6\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$\frac{7\sqrt{3}}{6\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\frac{7\sqrt{3}}{6\times 3}$$

Multiply 6 and 3 to get 18.

$$\frac{7\sqrt{3}}{18}$$