Lutasin ang sqrt{1500*981/sin(80)}

$$\sqrt{ \frac{ 1500 \times 981 }{ \sin ( 80 ) } }$$

I-evaluate

$$\frac{375000000\sqrt{40254016904374002}}{61550484563263}\approx 1222.37484406$$

Mga Hakbang ng Solution

Evaluate trigonometric functions in the problem

$$\sqrt{\frac{1500 \cdot 981}{0.984807753012208}}$$

I-multiply ang 1500 at 981 para makuha ang 1471500.

$$\sqrt{\frac{1471500}{0.984807753012208}}$$

I-expand ang \frac{1471500}{0.984807753012208} sa pamamagitan ng pag-multiply sa parehong numerator at denominator ng 1000000000000000.

$$\sqrt{\frac{1471500000000000000000}{984807753012208}}$$

Bawasan ang fraction \frac{1471500000000000000000}{984807753012208} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 16.

$$\sqrt{\frac{91968750000000000000}{61550484563263}}$$

I-rewrite ang square root ng division na \sqrt{\frac{91968750000000000000}{61550484563263}} bilang division ng mga square root na \frac{\sqrt{91968750000000000000}}{\sqrt{61550484563263}}.

$$\frac{\sqrt{91968750000000000000}}{\sqrt{61550484563263}}$$

I-factor out ang 91968750000000000000=375000000^{2}\times 654. I-rewrite ang square root ng product na \sqrt{375000000^{2}\times 654} bilang product ng mga square root na \sqrt{375000000^{2}}\sqrt{654}. Kunin ang square root ng 375000000^{2}.

$$\frac{375000000\sqrt{654}}{\sqrt{61550484563263}}$$

I-rationalize ang denominator ng \frac{375000000\sqrt{654}}{\sqrt{61550484563263}} sa pamamagitan ng pag-multiply ng numerator at denominator sa \sqrt{61550484563263}.

$$\frac{375000000\sqrt{654}\sqrt{61550484563263}}{\left(\sqrt{61550484563263}\right)^{2}}$$

Ang square ng \sqrt{61550484563263} ay 61550484563263.

$$\frac{375000000\sqrt{654}\sqrt{61550484563263}}{61550484563263}$$

Para i-multiply ang \sqrt{654} at \sqrt{61550484563263}, i-multiply ang mga numero sa ilalim ng square root.

$$\frac{375000000\sqrt{40254016904374002}}{61550484563263}$$