Solve 100*sqrt{99^2-3*99+2/99^2-1}

$$100 \times \sqrt{ \frac{ { 99 }^{ 2 } -3 \times 99+2 }{ { 99 }^{ 2 } -1 } }$$

Evaluate

$$10\sqrt{97}\approx 98.488578018$$

Solution Steps

Calculate 99 to the power of 2 and get 9801.

$$100\sqrt{\frac{9801-3\times 99+2}{99^{2}-1}}$$

Multiply 3 and 99 to get 297.

$$100\sqrt{\frac{9801-297+2}{99^{2}-1}}$$

Subtract 297 from 9801 to get 9504.

$$100\sqrt{\frac{9504+2}{99^{2}-1}}$$

Add 9504 and 2 to get 9506.

$$100\sqrt{\frac{9506}{99^{2}-1}}$$

Calculate 99 to the power of 2 and get 9801.

$$100\sqrt{\frac{9506}{9801-1}}$$

Subtract 1 from 9801 to get 9800.

$$100\sqrt{\frac{9506}{9800}}$$

Reduce the fraction \frac{9506}{9800} to lowest terms by extracting and canceling out 98.

$$100\sqrt{\frac{97}{100}}$$

Rewrite the square root of the division \sqrt{\frac{97}{100}} as the division of square roots \frac{\sqrt{97}}{\sqrt{100}}.

$$100\times \frac{\sqrt{97}}{\sqrt{100}}$$

Calculate the square root of 100 and get 10.

$$100\times \frac{\sqrt{97}}{10}$$

Cancel out 10, the greatest common factor in 100 and 10.

$$10\sqrt{97}$$