Solve 14*5+4sqrt{5225}*855/4152

$$14 \times 5+4 \sqrt{ 5225 } \times \frac{ 855 }{ 4152 }$$

Evaluate

$$\frac{1425\sqrt{209}}{346}+70\approx 129.540422023$$

Solution Steps

Multiply 14 and 5 to get 70.

$$70+4\sqrt{5225}\times \frac{855}{4152}$$

Factor 5225=5^{2}\times 209. Rewrite the square root of the product \sqrt{5^{2}\times 209} as the product of square roots \sqrt{5^{2}}\sqrt{209}. Take the square root of 5^{2}.

$$70+4\times 5\sqrt{209}\times \frac{855}{4152}$$

Multiply 4 and 5 to get 20.

$$70+20\sqrt{209}\times \frac{855}{4152}$$

Reduce the fraction \frac{855}{4152} to lowest terms by extracting and canceling out 3.

$$70+20\sqrt{209}\times \frac{285}{1384}$$

Express 20\times \frac{285}{1384} as a single fraction.

$$70+\frac{20\times 285}{1384}\sqrt{209}$$

Multiply 20 and 285 to get 5700.

$$70+\frac{5700}{1384}\sqrt{209}$$

Reduce the fraction \frac{5700}{1384} to lowest terms by extracting and canceling out 4.

$$70+\frac{1425}{346}\sqrt{209}$$

Factor

$$\frac{5 {(285 \sqrt{209} + 4844)}}{346} = 129.54042202338545$$