Solve 0.60-0.6/sqrt{frac{(0.6)(0.6){409}}}

$$\frac { 0.60 - 0.6 } { \sqrt { \frac { ( 0.6 ) ( 0.6 ) } { 409 } } }$$

Evaluate

$$0$$

Solution Steps

Subtract 0.6 from 0.6 to get 0.

$$\frac{0}{\sqrt{\frac{0.6\times 0.6}{409}}}$$

Multiply 0.6 and 0.6 to get 0.36.

$$\frac{0}{\sqrt{\frac{0.36}{409}}}$$

Expand \frac{0.36}{409} by multiplying both numerator and the denominator by 100.

$$\frac{0}{\sqrt{\frac{36}{40900}}}$$

Reduce the fraction \frac{36}{40900} to lowest terms by extracting and canceling out 4.

$$\frac{0}{\sqrt{\frac{9}{10225}}}$$

Rewrite the square root of the division \sqrt{\frac{9}{10225}} as the division of square roots \frac{\sqrt{9}}{\sqrt{10225}}.

$$\frac{0}{\frac{\sqrt{9}}{\sqrt{10225}}}$$

Calculate the square root of 9 and get 3.

$$\frac{0}{\frac{3}{\sqrt{10225}}}$$

Factor 10225=5^{2}\times 409. Rewrite the square root of the product \sqrt{5^{2}\times 409} as the product of square roots \sqrt{5^{2}}\sqrt{409}. Take the square root of 5^{2}.

$$\frac{0}{\frac{3}{5\sqrt{409}}}$$

Rationalize the denominator of \frac{3}{5\sqrt{409}} by multiplying numerator and denominator by \sqrt{409}.

$$\frac{0}{\frac{3\sqrt{409}}{5\left(\sqrt{409}\right)^{2}}}$$

The square of \sqrt{409} is 409.

$$\frac{0}{\frac{3\sqrt{409}}{5\times 409}}$$

Multiply 5 and 409 to get 2045.

$$\frac{0}{\frac{3\sqrt{409}}{2045}}$$

Divide 0 by \frac{3\sqrt{409}}{2045} by multiplying 0 by the reciprocal of \frac{3\sqrt{409}}{2045}.

$$\frac{0\times 2045}{3\sqrt{409}}$$

Cancel out 3 in both numerator and denominator.

$$\frac{0}{\sqrt{409}}$$

Zero divided by any non-zero term gives zero.

$$0$$

Factor

$$0$$