Solve -sqrt{900/41}+10

$$- \sqrt { \frac { 900 } { 41 } } + 10$$

Evaluate

$$-\frac{30\sqrt{41}}{41}+10\approx 5.314787143$$

Short Solution Steps

Rewrite the square root of the division \sqrt{\frac{900}{41}} as the division of square roots \frac{\sqrt{900}}{\sqrt{41}}.

$$-\frac{\sqrt{900}}{\sqrt{41}}+10$$

Calculate the square root of 900 and get 30.

$$-\frac{30}{\sqrt{41}}+10$$

Rationalize the denominator of \frac{30}{\sqrt{41}} by multiplying numerator and denominator by \sqrt{41}.

$$-\frac{30\sqrt{41}}{\left(\sqrt{41}\right)^{2}}+10$$

The square of \sqrt{41} is 41.

$$-\frac{30\sqrt{41}}{41}+10$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 10 times \frac{41}{41}.

$$-\frac{30\sqrt{41}}{41}+\frac{10\times 41}{41}$$

Since -\frac{30\sqrt{41}}{41} and \frac{10\times 41}{41} have the same denominator, add them by adding their numerators.

$$\frac{-30\sqrt{41}+10\times 41}{41}$$

Do the multiplications in -30\sqrt{41}+10\times 41.

$$\frac{-30\sqrt{41}+410}{41}$$