Solve 711+196*34/sqrt{46224}

$$711 + 196 \times \frac { 34 } { \sqrt { 46224 } }$$

Evaluate

$$\frac{1666\sqrt{321}}{963}+711\approx 741.995684109$$

Short Solution Steps

Factor 46224=12^{2}\times 321. Rewrite the square root of the product \sqrt{12^{2}\times 321} as the product of square roots \sqrt{12^{2}}\sqrt{321}. Take the square root of 12^{2}.

$$711+196\times \frac{34}{12\sqrt{321}}$$

Rationalize the denominator of \frac{34}{12\sqrt{321}} by multiplying numerator and denominator by \sqrt{321}.

$$711+196\times \frac{34\sqrt{321}}{12\left(\sqrt{321}\right)^{2}}$$

The square of \sqrt{321} is 321.

$$711+196\times \frac{34\sqrt{321}}{12\times 321}$$

Cancel out 2 in both numerator and denominator.

$$711+196\times \frac{17\sqrt{321}}{6\times 321}$$

Multiply 6 and 321 to get 1926.

$$711+196\times \frac{17\sqrt{321}}{1926}$$

Express 196\times \frac{17\sqrt{321}}{1926} as a single fraction.

$$711+\frac{196\times 17\sqrt{321}}{1926}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 711 times \frac{1926}{1926}.

$$\frac{711\times 1926}{1926}+\frac{196\times 17\sqrt{321}}{1926}$$

Since \frac{711\times 1926}{1926} and \frac{196\times 17\sqrt{321}}{1926} have the same denominator, add them by adding their numerators.

$$\frac{711\times 1926+196\times 17\sqrt{321}}{1926}$$

Do the multiplications in 711\times 1926+196\times 17\sqrt{321}.

$$\frac{1369386+3332\sqrt{321}}{1926}$$