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

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

Evaluate

$$\frac{179\sqrt{127442}}{2}\approx 31950.622536971$$

Solution Steps

Calculate 179 to the power of 2 and get 32041.

$$179\sqrt{\frac{32041+4\times 1\times 7920}{2\times 1}}$$

Multiply 4 and 1 to get 4.

$$179\sqrt{\frac{32041+4\times 7920}{2\times 1}}$$

Multiply 4 and 7920 to get 31680.

$$179\sqrt{\frac{32041+31680}{2\times 1}}$$

Add 32041 and 31680 to get 63721.

$$179\sqrt{\frac{63721}{2\times 1}}$$

Multiply 2 and 1 to get 2.

$$179\sqrt{\frac{63721}{2}}$$

Rewrite the square root of the division \sqrt{\frac{63721}{2}} as the division of square roots \frac{\sqrt{63721}}{\sqrt{2}}.

$$179\times \frac{\sqrt{63721}}{\sqrt{2}}$$

Rationalize the denominator of \frac{\sqrt{63721}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$179\times \frac{\sqrt{63721}\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$179\times \frac{\sqrt{63721}\sqrt{2}}{2}$$

To multiply \sqrt{63721} and \sqrt{2}, multiply the numbers under the square root.

$$179\times \frac{\sqrt{127442}}{2}$$

Express 179\times \frac{\sqrt{127442}}{2} as a single fraction.

$$\frac{179\sqrt{127442}}{2}$$