Solve frac{16sqrt{963}}{sqrt{38}}

$$\frac { 16 \sqrt { 963 } } { \sqrt { 38 } }$$

Evaluate

$$\frac{24\sqrt{4066}}{19}\approx 80.545508549$$

Solution Steps

Factor 963=3^{2}\times 107. Rewrite the square root of the product \sqrt{3^{2}\times 107} as the product of square roots \sqrt{3^{2}}\sqrt{107}. Take the square root of 3^{2}.

$$\frac{16\times 3\sqrt{107}}{\sqrt{38}}$$

Multiply 16 and 3 to get 48.

$$\frac{48\sqrt{107}}{\sqrt{38}}$$

Rationalize the denominator of \frac{48\sqrt{107}}{\sqrt{38}} by multiplying numerator and denominator by \sqrt{38}.

$$\frac{48\sqrt{107}\sqrt{38}}{\left(\sqrt{38}\right)^{2}}$$

The square of \sqrt{38} is 38.

$$\frac{48\sqrt{107}\sqrt{38}}{38}$$

To multiply \sqrt{107} and \sqrt{38}, multiply the numbers under the square root.

$$\frac{48\sqrt{4066}}{38}$$

Divide 48\sqrt{4066} by 38 to get \frac{24}{19}\sqrt{4066}.

$$\frac{24}{19}\sqrt{4066}$$