Solve frac{sqrt{17}-3/4}{3/4sqrt{15}}

$$\frac{ \sqrt{ 17 } - \frac{ 3 }{ 4 } }{ \frac{ 3 }{ 4 } \sqrt{ 15 } }$$

Evaluate

$$\frac{4\sqrt{255}}{45}-\frac{\sqrt{15}}{15}\approx 1.161242837$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{17}-\frac{3}{4}}{\frac{3}{4}\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{\left(\sqrt{17}-\frac{3}{4}\right)\sqrt{15}}{\frac{3}{4}\left(\sqrt{15}\right)^{2}}$$

The square of \sqrt{15} is 15.

$$\frac{\left(\sqrt{17}-\frac{3}{4}\right)\sqrt{15}}{\frac{3}{4}\times 15}$$

Express \frac{3}{4}\times 15 as a single fraction.

$$\frac{\left(\sqrt{17}-\frac{3}{4}\right)\sqrt{15}}{\frac{3\times 15}{4}}$$

Multiply 3 and 15 to get 45.

$$\frac{\left(\sqrt{17}-\frac{3}{4}\right)\sqrt{15}}{\frac{45}{4}}$$

Divide \left(\sqrt{17}-\frac{3}{4}\right)\sqrt{15} by \frac{45}{4} by multiplying \left(\sqrt{17}-\frac{3}{4}\right)\sqrt{15} by the reciprocal of \frac{45}{4}.

$$\frac{\left(\sqrt{17}-\frac{3}{4}\right)\sqrt{15}\times 4}{45}$$

Use the distributive property to multiply \sqrt{17}-\frac{3}{4} by \sqrt{15}.

$$\frac{\left(\sqrt{17}\sqrt{15}-\frac{3}{4}\sqrt{15}\right)\times 4}{45}$$

To multiply \sqrt{17} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{\left(\sqrt{255}-\frac{3}{4}\sqrt{15}\right)\times 4}{45}$$

Use the distributive property to multiply \sqrt{255}-\frac{3}{4}\sqrt{15} by 4.

$$\frac{4\sqrt{255}-\frac{3}{4}\sqrt{15}\times 4}{45}$$

Cancel out 4 and 4.

$$\frac{4\sqrt{255}-3\sqrt{15}}{45}$$

Factor

$$\frac{\sqrt{15} {(4 \sqrt{17} - 3)}}{45} = 1.1612428367125112$$