Solve 0:68-0.15/sqrt{(0.34875*0.65125/frac{1{300}+1/300)}}

$$\frac { 0 : 68 - 0.15 } { \sqrt { ( 0.34875 \times 0.65125 / \frac { 1 } { 300 } + \frac { 1 } { 300 } ) } }$$

Evaluate

$$-\frac{12\sqrt{3924885}}{1308295}\approx -0.018171427$$

Solution Steps

Zero divided by any non-zero number gives zero.

$$\frac{0-0.15}{\sqrt{\frac{0.34875\times 0.65125}{\frac{1}{300}}+\frac{1}{300}}}$$

Subtract 0.15 from 0 to get -0.15.

$$\frac{-0.15}{\sqrt{\frac{0.34875\times 0.65125}{\frac{1}{300}}+\frac{1}{300}}}$$

Multiply 0.34875 and 0.65125 to get 0.2271234375.

$$\frac{-0.15}{\sqrt{\frac{0.2271234375}{\frac{1}{300}}+\frac{1}{300}}}$$

Divide 0.2271234375 by \frac{1}{300} by multiplying 0.2271234375 by the reciprocal of \frac{1}{300}.

$$\frac{-0.15}{\sqrt{0.2271234375\times 300+\frac{1}{300}}}$$

Multiply 0.2271234375 and 300 to get 68.13703125.

$$\frac{-0.15}{\sqrt{68.13703125+\frac{1}{300}}}$$

Convert decimal number 68.13703125 to fraction \frac{6813703125}{100000000}. Reduce the fraction \frac{6813703125}{100000000} to lowest terms by extracting and canceling out 15625.

$$\frac{-0.15}{\sqrt{\frac{436077}{6400}+\frac{1}{300}}}$$

Least common multiple of 6400 and 300 is 19200. Convert \frac{436077}{6400} and \frac{1}{300} to fractions with denominator 19200.

$$\frac{-0.15}{\sqrt{\frac{1308231}{19200}+\frac{64}{19200}}}$$

Since \frac{1308231}{19200} and \frac{64}{19200} have the same denominator, add them by adding their numerators.

$$\frac{-0.15}{\sqrt{\frac{1308231+64}{19200}}}$$

Add 1308231 and 64 to get 1308295.

$$\frac{-0.15}{\sqrt{\frac{1308295}{19200}}}$$

Reduce the fraction \frac{1308295}{19200} to lowest terms by extracting and canceling out 5.

$$\frac{-0.15}{\sqrt{\frac{261659}{3840}}}$$

Rewrite the square root of the division \sqrt{\frac{261659}{3840}} as the division of square roots \frac{\sqrt{261659}}{\sqrt{3840}}.

$$\frac{-0.15}{\frac{\sqrt{261659}}{\sqrt{3840}}}$$

Factor 3840=16^{2}\times 15. Rewrite the square root of the product \sqrt{16^{2}\times 15} as the product of square roots \sqrt{16^{2}}\sqrt{15}. Take the square root of 16^{2}.

$$\frac{-0.15}{\frac{\sqrt{261659}}{16\sqrt{15}}}$$

Rationalize the denominator of \frac{\sqrt{261659}}{16\sqrt{15}} by multiplying numerator and denominator by \sqrt{15}.

$$\frac{-0.15}{\frac{\sqrt{261659}\sqrt{15}}{16\left(\sqrt{15}\right)^{2}}}$$

The square of \sqrt{15} is 15.

$$\frac{-0.15}{\frac{\sqrt{261659}\sqrt{15}}{16\times 15}}$$

To multiply \sqrt{261659} and \sqrt{15}, multiply the numbers under the square root.

$$\frac{-0.15}{\frac{\sqrt{3924885}}{16\times 15}}$$

Multiply 16 and 15 to get 240.

$$\frac{-0.15}{\frac{\sqrt{3924885}}{240}}$$

Divide -0.15 by \frac{\sqrt{3924885}}{240} by multiplying -0.15 by the reciprocal of \frac{\sqrt{3924885}}{240}.

$$\frac{-0.15\times 240}{\sqrt{3924885}}$$

Rationalize the denominator of \frac{-0.15\times 240}{\sqrt{3924885}} by multiplying numerator and denominator by \sqrt{3924885}.

$$\frac{-0.15\times 240\sqrt{3924885}}{\left(\sqrt{3924885}\right)^{2}}$$

The square of \sqrt{3924885} is 3924885.

$$\frac{-0.15\times 240\sqrt{3924885}}{3924885}$$

Multiply -0.15 and 240 to get -36.

$$\frac{-36\sqrt{3924885}}{3924885}$$

Divide -36\sqrt{3924885} by 3924885 to get -\frac{12}{1308295}\sqrt{3924885}.

$$-\frac{12}{1308295}\sqrt{3924885}$$