Solve 25-sqrt{1/9-frac{11{3}}}

$$25- \sqrt{ \frac{ 1 }{ 9- \frac{ 11 }{ 3 } } }$$

Evaluate

$$-\frac{\sqrt{3}}{4}+25\approx 24.566987298$$

Short Solution Steps

Convert 9 to fraction \frac{27}{3}.

$$25-\sqrt{\frac{1}{\frac{27}{3}-\frac{11}{3}}}$$

Since \frac{27}{3} and \frac{11}{3} have the same denominator, subtract them by subtracting their numerators.

$$25-\sqrt{\frac{1}{\frac{27-11}{3}}}$$

Subtract 11 from 27 to get 16.

$$25-\sqrt{\frac{1}{\frac{16}{3}}}$$

Divide 1 by \frac{16}{3} by multiplying 1 by the reciprocal of \frac{16}{3}.

$$25-\sqrt{1\times \frac{3}{16}}$$

Multiply 1 and \frac{3}{16} to get \frac{3}{16}.

$$25-\sqrt{\frac{3}{16}}$$

Rewrite the square root of the division \sqrt{\frac{3}{16}} as the division of square roots \frac{\sqrt{3}}{\sqrt{16}}.

$$25-\frac{\sqrt{3}}{\sqrt{16}}$$

Calculate the square root of 16 and get 4.

$$25-\frac{\sqrt{3}}{4}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 25 times \frac{4}{4}.

$$\frac{25\times 4}{4}-\frac{\sqrt{3}}{4}$$

Since \frac{25\times 4}{4} and \frac{\sqrt{3}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{25\times 4-\sqrt{3}}{4}$$

Do the multiplications in 25\times 4-\sqrt{3}.

$$\frac{100-\sqrt{3}}{4}$$