Solve 711-196*34^2/sqrt{46224}

$$711 - 196 \times \frac { 34 ^ { 2 } } { \sqrt { 46224 } }$$

Evaluate

$$-\frac{56644\sqrt{321}}{963}+711\approx -342.853259697$$

Short Solution Steps

Calculate 34 to the power of 2 and get 1156.

$$711-196\times \frac{1156}{\sqrt{46224}}$$

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}.

$$711-196\times \frac{1156}{12\sqrt{321}}$$

Rationalize the denominator of \frac{1156}{12\sqrt{321}} by multiplying numerator and denominator by \sqrt{321}.

$$711-196\times \frac{1156\sqrt{321}}{12\left(\sqrt{321}\right)^{2}}$$

The square of \sqrt{321} is 321.

$$711-196\times \frac{1156\sqrt{321}}{12\times 321}$$

Cancel out 4 in both numerator and denominator.

$$711-196\times \frac{289\sqrt{321}}{3\times 321}$$

Multiply 3 and 321 to get 963.

$$711-196\times \frac{289\sqrt{321}}{963}$$

Express 196\times \frac{289\sqrt{321}}{963} as a single fraction.

$$711-\frac{196\times 289\sqrt{321}}{963}$$

Multiply 196 and 289 to get 56644.

$$711-\frac{56644\sqrt{321}}{963}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 711 times \frac{963}{963}.

$$\frac{711\times 963}{963}-\frac{56644\sqrt{321}}{963}$$

Since \frac{711\times 963}{963} and \frac{56644\sqrt{321}}{963} have the same denominator, subtract them by subtracting their numerators.

$$\frac{711\times 963-56644\sqrt{321}}{963}$$

Do the multiplications in 711\times 963-56644\sqrt{321}.

$$\frac{684693-56644\sqrt{321}}{963}$$