Solve sqrt{75+(4.5^2+40)/6.5*10^4}

$$\sqrt { \frac { 75 + ( 4.5 ^ { 2 } + 40 ) } { 6.5 \times 10 ^ { 4 } } }$$

Evaluate

$$\frac{\sqrt{14066}}{2600}\approx 0.045615449$$

Solution Steps

Calculate 4.5 to the power of 2 and get 20.25.

$$\sqrt{\frac{75+20.25+40}{6.5\times 10^{4}}}$$

Add 75 and 20.25 to get 95.25.

$$\sqrt{\frac{95.25+40}{6.5\times 10^{4}}}$$

Add 95.25 and 40 to get 135.25.

$$\sqrt{\frac{135.25}{6.5\times 10^{4}}}$$

Calculate 10 to the power of 4 and get 10000.

$$\sqrt{\frac{135.25}{6.5\times 10000}}$$

Multiply 6.5 and 10000 to get 65000.

$$\sqrt{\frac{135.25}{65000}}$$

Expand \frac{135.25}{65000} by multiplying both numerator and the denominator by 100.

$$\sqrt{\frac{13525}{6500000}}$$

Reduce the fraction \frac{13525}{6500000} to lowest terms by extracting and canceling out 25.

$$\sqrt{\frac{541}{260000}}$$

Rewrite the square root of the division \sqrt{\frac{541}{260000}} as the division of square roots \frac{\sqrt{541}}{\sqrt{260000}}.

$$\frac{\sqrt{541}}{\sqrt{260000}}$$

Factor 260000=100^{2}\times 26. Rewrite the square root of the product \sqrt{100^{2}\times 26} as the product of square roots \sqrt{100^{2}}\sqrt{26}. Take the square root of 100^{2}.

$$\frac{\sqrt{541}}{100\sqrt{26}}$$

Rationalize the denominator of \frac{\sqrt{541}}{100\sqrt{26}} by multiplying numerator and denominator by \sqrt{26}.

$$\frac{\sqrt{541}\sqrt{26}}{100\left(\sqrt{26}\right)^{2}}$$

The square of \sqrt{26} is 26.

$$\frac{\sqrt{541}\sqrt{26}}{100\times 26}$$

To multiply \sqrt{541} and \sqrt{26}, multiply the numbers under the square root.

$$\frac{\sqrt{14066}}{100\times 26}$$

Multiply 100 and 26 to get 2600.

$$\frac{\sqrt{14066}}{2600}$$