Solve 0802+10sqrt{13/8400}

$$0802+10 \sqrt{ \frac{ 13 }{ 8400 } }$$

Evaluate

$$\frac{\sqrt{273}}{42}\approx 0.393397896$$

Solution Steps

Multiply 0 and 802 to get 0.

$$0+10\sqrt{\frac{13}{8400}}$$

Rewrite the square root of the division \sqrt{\frac{13}{8400}} as the division of square roots \frac{\sqrt{13}}{\sqrt{8400}}.

$$0+10\times \frac{\sqrt{13}}{\sqrt{8400}}$$

Factor 8400=20^{2}\times 21. Rewrite the square root of the product \sqrt{20^{2}\times 21} as the product of square roots \sqrt{20^{2}}\sqrt{21}. Take the square root of 20^{2}.

$$0+10\times \frac{\sqrt{13}}{20\sqrt{21}}$$

Rationalize the denominator of \frac{\sqrt{13}}{20\sqrt{21}} by multiplying numerator and denominator by \sqrt{21}.

$$0+10\times \frac{\sqrt{13}\sqrt{21}}{20\left(\sqrt{21}\right)^{2}}$$

The square of \sqrt{21} is 21.

$$0+10\times \frac{\sqrt{13}\sqrt{21}}{20\times 21}$$

To multiply \sqrt{13} and \sqrt{21}, multiply the numbers under the square root.

$$0+10\times \frac{\sqrt{273}}{20\times 21}$$

Multiply 20 and 21 to get 420.

$$0+10\times \frac{\sqrt{273}}{420}$$

Cancel out 420, the greatest common factor in 10 and 420.

$$0+\frac{\sqrt{273}}{42}$$

Anything plus zero gives itself.

$$\frac{\sqrt{273}}{42}$$