Solve sqrt{1500*9.81/sin(80)}

$$\sqrt{ \frac{ 1500 \times 9.81 }{ \sin ( 80 ) } }$$

Evaluate

$$\frac{37500000\sqrt{40254016904374002}}{61550484563263}\approx 122.237484406$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\sqrt{\frac{1500 \cdot 9.81}{0.984807753012208}}$$

Multiply 1500 and 9.81 to get 14715.

$$\sqrt{\frac{14715}{0.984807753012208}}$$

Expand \frac{14715}{0.984807753012208} by multiplying both numerator and the denominator by 1000000000000000.

$$\sqrt{\frac{14715000000000000000}{984807753012208}}$$

Reduce the fraction \frac{14715000000000000000}{984807753012208} to lowest terms by extracting and canceling out 16.

$$\sqrt{\frac{919687500000000000}{61550484563263}}$$

Rewrite the square root of the division \sqrt{\frac{919687500000000000}{61550484563263}} as the division of square roots \frac{\sqrt{919687500000000000}}{\sqrt{61550484563263}}.

$$\frac{\sqrt{919687500000000000}}{\sqrt{61550484563263}}$$

Factor 919687500000000000=37500000^{2}\times 654. Rewrite the square root of the product \sqrt{37500000^{2}\times 654} as the product of square roots \sqrt{37500000^{2}}\sqrt{654}. Take the square root of 37500000^{2}.

$$\frac{37500000\sqrt{654}}{\sqrt{61550484563263}}$$

Rationalize the denominator of \frac{37500000\sqrt{654}}{\sqrt{61550484563263}} by multiplying numerator and denominator by \sqrt{61550484563263}.

$$\frac{37500000\sqrt{654}\sqrt{61550484563263}}{\left(\sqrt{61550484563263}\right)^{2}}$$

The square of \sqrt{61550484563263} is 61550484563263.

$$\frac{37500000\sqrt{654}\sqrt{61550484563263}}{61550484563263}$$

To multiply \sqrt{654} and \sqrt{61550484563263}, multiply the numbers under the square root.

$$\frac{37500000\sqrt{40254016904374002}}{61550484563263}$$