Solve 2sqrt{100.98*(50.98-49/4/50.98})

$$2 \sqrt{ 100.98 \times ( \frac{ 50.98- \frac{ 49 }{ 4 } }{ 50.98 } } )$$

Evaluate

$$\frac{9\sqrt{615371933}}{12745}\approx 17.517475218$$

Solution Steps

Convert decimal number 50.98 to fraction \frac{5098}{100}. Reduce the fraction \frac{5098}{100} to lowest terms by extracting and canceling out 2.

$$2\sqrt{100.98\times \frac{\frac{2549}{50}-\frac{49}{4}}{50.98}}$$

Least common multiple of 50 and 4 is 100. Convert \frac{2549}{50} and \frac{49}{4} to fractions with denominator 100.

$$2\sqrt{100.98\times \frac{\frac{5098}{100}-\frac{1225}{100}}{50.98}}$$

Since \frac{5098}{100} and \frac{1225}{100} have the same denominator, subtract them by subtracting their numerators.

$$2\sqrt{100.98\times \frac{\frac{5098-1225}{100}}{50.98}}$$

Subtract 1225 from 5098 to get 3873.

$$2\sqrt{100.98\times \frac{\frac{3873}{100}}{50.98}}$$

Express \frac{\frac{3873}{100}}{50.98} as a single fraction.

$$2\sqrt{100.98\times \frac{3873}{100\times 50.98}}$$

Multiply 100 and 50.98 to get 5098.

$$2\sqrt{100.98\times \frac{3873}{5098}}$$

Convert decimal number 100.98 to fraction \frac{10098}{100}. Reduce the fraction \frac{10098}{100} to lowest terms by extracting and canceling out 2.

$$2\sqrt{\frac{5049}{50}\times \frac{3873}{5098}}$$

Multiply \frac{5049}{50} times \frac{3873}{5098} by multiplying numerator times numerator and denominator times denominator.

$$2\sqrt{\frac{5049\times 3873}{50\times 5098}}$$

Do the multiplications in the fraction \frac{5049\times 3873}{50\times 5098}.

$$2\sqrt{\frac{19554777}{254900}}$$

Rewrite the square root of the division \sqrt{\frac{19554777}{254900}} as the division of square roots \frac{\sqrt{19554777}}{\sqrt{254900}}.

$$2\times \frac{\sqrt{19554777}}{\sqrt{254900}}$$

Factor 19554777=9^{2}\times 241417. Rewrite the square root of the product \sqrt{9^{2}\times 241417} as the product of square roots \sqrt{9^{2}}\sqrt{241417}. Take the square root of 9^{2}.

$$2\times \frac{9\sqrt{241417}}{\sqrt{254900}}$$

Factor 254900=10^{2}\times 2549. Rewrite the square root of the product \sqrt{10^{2}\times 2549} as the product of square roots \sqrt{10^{2}}\sqrt{2549}. Take the square root of 10^{2}.

$$2\times \frac{9\sqrt{241417}}{10\sqrt{2549}}$$

Rationalize the denominator of \frac{9\sqrt{241417}}{10\sqrt{2549}} by multiplying numerator and denominator by \sqrt{2549}.

$$2\times \frac{9\sqrt{241417}\sqrt{2549}}{10\left(\sqrt{2549}\right)^{2}}$$

The square of \sqrt{2549} is 2549.

$$2\times \frac{9\sqrt{241417}\sqrt{2549}}{10\times 2549}$$

To multiply \sqrt{241417} and \sqrt{2549}, multiply the numbers under the square root.

$$2\times \frac{9\sqrt{615371933}}{10\times 2549}$$

Multiply 10 and 2549 to get 25490.

$$2\times \frac{9\sqrt{615371933}}{25490}$$

Cancel out 25490, the greatest common factor in 2 and 25490.

$$\frac{9\sqrt{615371933}}{12745}$$