Solve sqrt{279/448}

$$\sqrt { \frac { 279 } { 448 } }$$

Evaluate

$$\frac{3\sqrt{217}}{56}\approx 0.789156421$$

Solution Steps

Rewrite the square root of the division \sqrt{\frac{279}{448}} as the division of square roots \frac{\sqrt{279}}{\sqrt{448}}.

$$\frac{\sqrt{279}}{\sqrt{448}}$$

Factor 279=3^{2}\times 31. Rewrite the square root of the product \sqrt{3^{2}\times 31} as the product of square roots \sqrt{3^{2}}\sqrt{31}. Take the square root of 3^{2}.

$$\frac{3\sqrt{31}}{\sqrt{448}}$$

Factor 448=8^{2}\times 7. Rewrite the square root of the product \sqrt{8^{2}\times 7} as the product of square roots \sqrt{8^{2}}\sqrt{7}. Take the square root of 8^{2}.

$$\frac{3\sqrt{31}}{8\sqrt{7}}$$

Rationalize the denominator of \frac{3\sqrt{31}}{8\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$\frac{3\sqrt{31}\sqrt{7}}{8\left(\sqrt{7}\right)^{2}}$$

The square of \sqrt{7} is 7.

$$\frac{3\sqrt{31}\sqrt{7}}{8\times 7}$$

To multiply \sqrt{31} and \sqrt{7}, multiply the numbers under the square root.

$$\frac{3\sqrt{217}}{8\times 7}$$

Multiply 8 and 7 to get 56.

$$\frac{3\sqrt{217}}{56}$$