Solve sqrt{187.3324*1.5^2/20+(1.3^2}

$$\sqrt{ \frac{ 187.3324 \times { 1.5 }^{ 2 } }{ 20 } +( { 1.3 }^{ 2 } }$$

Evaluate

$$\frac{\sqrt{22764895}}{1000}\approx 4.771257172$$

Solution Steps

Calculate 1.5 to the power of 2 and get 2.25.

$$\sqrt{\frac{187.3324\times 2.25}{20}+1.3^{2}}$$

Multiply 187.3324 and 2.25 to get 421.4979.

$$\sqrt{\frac{421.4979}{20}+1.3^{2}}$$

Expand \frac{421.4979}{20} by multiplying both numerator and the denominator by 10000.

$$\sqrt{\frac{4214979}{200000}+1.3^{2}}$$

Calculate 1.3 to the power of 2 and get 1.69.

$$\sqrt{\frac{4214979}{200000}+1.69}$$

Convert decimal number 1.69 to fraction \frac{169}{100}.

$$\sqrt{\frac{4214979}{200000}+\frac{169}{100}}$$

Least common multiple of 200000 and 100 is 200000. Convert \frac{4214979}{200000} and \frac{169}{100} to fractions with denominator 200000.

$$\sqrt{\frac{4214979}{200000}+\frac{338000}{200000}}$$

Since \frac{4214979}{200000} and \frac{338000}{200000} have the same denominator, add them by adding their numerators.

$$\sqrt{\frac{4214979+338000}{200000}}$$

Add 4214979 and 338000 to get 4552979.

$$\sqrt{\frac{4552979}{200000}}$$

Rewrite the square root of the division \sqrt{\frac{4552979}{200000}} as the division of square roots \frac{\sqrt{4552979}}{\sqrt{200000}}.

$$\frac{\sqrt{4552979}}{\sqrt{200000}}$$

Factor 200000=200^{2}\times 5. Rewrite the square root of the product \sqrt{200^{2}\times 5} as the product of square roots \sqrt{200^{2}}\sqrt{5}. Take the square root of 200^{2}.

$$\frac{\sqrt{4552979}}{200\sqrt{5}}$$

Rationalize the denominator of \frac{\sqrt{4552979}}{200\sqrt{5}} by multiplying numerator and denominator by \sqrt{5}.

$$\frac{\sqrt{4552979}\sqrt{5}}{200\left(\sqrt{5}\right)^{2}}$$

The square of \sqrt{5} is 5.

$$\frac{\sqrt{4552979}\sqrt{5}}{200\times 5}$$

To multiply \sqrt{4552979} and \sqrt{5}, multiply the numbers under the square root.

$$\frac{\sqrt{22764895}}{200\times 5}$$

Multiply 200 and 5 to get 1000.

$$\frac{\sqrt{22764895}}{1000}$$