Solve frac{sqrt{64+36}}{sqrt{64}*sqrt{38}}

$$\frac { \sqrt { 64 + 36 } } { \sqrt { 64 } \cdot \sqrt { 38 } }$$

Evaluate

$$\frac{5\sqrt{38}}{152}\approx 0.202776776$$

Solution Steps

Add 64 and 36 to get 100.

$$\frac{\sqrt{100}}{\sqrt{64}\sqrt{38}}$$

Calculate the square root of 100 and get 10.

$$\frac{10}{\sqrt{64}\sqrt{38}}$$

Calculate the square root of 64 and get 8.

$$\frac{10}{8\sqrt{38}}$$

Rationalize the denominator of \frac{10}{8\sqrt{38}} by multiplying numerator and denominator by \sqrt{38}.

$$\frac{10\sqrt{38}}{8\left(\sqrt{38}\right)^{2}}$$

The square of \sqrt{38} is 38.

$$\frac{10\sqrt{38}}{8\times 38}$$

Cancel out 2 in both numerator and denominator.

$$\frac{5\sqrt{38}}{4\times 38}$$

Multiply 4 and 38 to get 152.

$$\frac{5\sqrt{38}}{152}$$