Solve -179sqrt{179+4*1*7920/2*1}

$$-179 \sqrt{ \frac{ 179+4 \times 1 \times 7920 }{ 2 \times 1 } }$$

Evaluate

$$-\frac{179\sqrt{63718}}{2}\approx -22591.970022554$$

Solution Steps

Multiply 4 and 1 to get 4.

$$-179\sqrt{\frac{179+4\times 7920}{2}}$$

Multiply 4 and 7920 to get 31680.

$$-179\sqrt{\frac{179+31680}{2}}$$

Add 179 and 31680 to get 31859.

$$-179\sqrt{\frac{31859}{2}}$$

Rewrite the square root of the division \sqrt{\frac{31859}{2}} as the division of square roots \frac{\sqrt{31859}}{\sqrt{2}}.

$$-179\times \frac{\sqrt{31859}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{31859}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$-179\times \frac{\sqrt{31859}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-179\times \frac{\sqrt{31859}\sqrt{2}}{2}$$

To multiply \sqrt{31859} and \sqrt{2}, multiply the numbers under the square root.

$$-179\times \frac{\sqrt{63718}}{2}$$

Express -179\times \frac{\sqrt{63718}}{2} as a single fraction.

$$\frac{-179\sqrt{63718}}{2}$$