Solve 1/0.527sqrt{9.96*10^6}(1+0.02)+100

$$\frac{ 1 }{ 0.527 } \sqrt{ 9.96 \times { 10 }^{ 6 } } (1+0.02)+100$$

Evaluate

$$\frac{12000\sqrt{249}}{31}+100\approx 6208.284066346$$

Solution Steps

Expand \frac{1}{0.527} by multiplying both numerator and the denominator by 1000.

$$\frac{1000}{527}\sqrt{9.96\times 10^{6}}\left(1+0.02\right)+100$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{1000}{527}\sqrt{9.96\times 1000000}\left(1+0.02\right)+100$$

Multiply 9.96 and 1000000 to get 9960000.

$$\frac{1000}{527}\sqrt{9960000}\left(1+0.02\right)+100$$

Factor 9960000=200^{2}\times 249. Rewrite the square root of the product \sqrt{200^{2}\times 249} as the product of square roots \sqrt{200^{2}}\sqrt{249}. Take the square root of 200^{2}.

$$\frac{1000}{527}\times 200\sqrt{249}\left(1+0.02\right)+100$$

Express \frac{1000}{527}\times 200 as a single fraction.

$$\frac{1000\times 200}{527}\sqrt{249}\left(1+0.02\right)+100$$

Multiply 1000 and 200 to get 200000.

$$\frac{200000}{527}\sqrt{249}\left(1+0.02\right)+100$$

Add 1 and 0.02 to get 1.02.

$$\frac{200000}{527}\sqrt{249}\times 1.02+100$$

Convert decimal number 1.02 to fraction \frac{102}{100}. Reduce the fraction \frac{102}{100} to lowest terms by extracting and canceling out 2.

$$\frac{200000}{527}\sqrt{249}\times \frac{51}{50}+100$$

Multiply \frac{200000}{527} times \frac{51}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{200000\times 51}{527\times 50}\sqrt{249}+100$$

Do the multiplications in the fraction \frac{200000\times 51}{527\times 50}.

$$\frac{10200000}{26350}\sqrt{249}+100$$

Reduce the fraction \frac{10200000}{26350} to lowest terms by extracting and canceling out 850.

$$\frac{12000}{31}\sqrt{249}+100$$