Solve 11.25-13.4/4.245913sqrt{(4)(5)/9(9-1)}

$$\frac { 11.25 - 13.4 } { 4.245913 } \sqrt { \frac { ( 4 ) ( 5 ) } { 9 ( 9 - 1 ) } }$$

Evaluate

$$-\frac{1075000\sqrt{10}}{12737739}\approx -0.266880055$$

Solution Steps

Subtract 13.4 from 11.25 to get -2.15.

$$\frac{-2.15}{4.245913}\sqrt{\frac{4\times 5}{9\left(9-1\right)}}$$

Expand \frac{-2.15}{4.245913} by multiplying both numerator and the denominator by 1000000.

$$\frac{-2150000}{4245913}\sqrt{\frac{4\times 5}{9\left(9-1\right)}}$$

Fraction \frac{-2150000}{4245913} can be rewritten as -\frac{2150000}{4245913} by extracting the negative sign.

$$-\frac{2150000}{4245913}\sqrt{\frac{4\times 5}{9\left(9-1\right)}}$$

Multiply 4 and 5 to get 20.

$$-\frac{2150000}{4245913}\sqrt{\frac{20}{9\left(9-1\right)}}$$

Subtract 1 from 9 to get 8.

$$-\frac{2150000}{4245913}\sqrt{\frac{20}{9\times 8}}$$

Multiply 9 and 8 to get 72.

$$-\frac{2150000}{4245913}\sqrt{\frac{20}{72}}$$

Reduce the fraction \frac{20}{72} to lowest terms by extracting and canceling out 4.

$$-\frac{2150000}{4245913}\sqrt{\frac{5}{18}}$$

Rewrite the square root of the division \sqrt{\frac{5}{18}} as the division of square roots \frac{\sqrt{5}}{\sqrt{18}}.

$$-\frac{2150000}{4245913}\times \frac{\sqrt{5}}{\sqrt{18}}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$-\frac{2150000}{4245913}\times \frac{\sqrt{5}}{3\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{5}}{3\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$-\frac{2150000}{4245913}\times \frac{\sqrt{5}\sqrt{2}}{3\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-\frac{2150000}{4245913}\times \frac{\sqrt{5}\sqrt{2}}{3\times 2}$$

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$-\frac{2150000}{4245913}\times \frac{\sqrt{10}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$-\frac{2150000}{4245913}\times \frac{\sqrt{10}}{6}$$

Multiply -\frac{2150000}{4245913} times \frac{\sqrt{10}}{6} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-2150000\sqrt{10}}{4245913\times 6}$$

Cancel out 2 in both numerator and denominator.

$$\frac{-1075000\sqrt{10}}{3\times 4245913}$$

Multiply 3 and 4245913 to get 12737739.

$$\frac{-1075000\sqrt{10}}{12737739}$$