Solve sqrt{750^2+1500^2-2*1500*750*(-1/2})==

$$\sqrt{ { 750 }^{ 2 } + { 1500 }^{ 2 } -2 \times 1500 \times 750 \times (- \frac{ 1 }{ 2 } } )==$$

Evaluate

$$750\sqrt{7}\approx 1984.313483298$$

Solution Steps

Calculate 750 to the power of 2 and get 562500.

$$\sqrt{562500+1500^{2}-2\times 1500\times 750\left(-\frac{1}{2}\right)}$$

Calculate 1500 to the power of 2 and get 2250000.

$$\sqrt{562500+2250000-2\times 1500\times 750\left(-\frac{1}{2}\right)}$$

Add 562500 and 2250000 to get 2812500.

$$\sqrt{2812500-2\times 1500\times 750\left(-\frac{1}{2}\right)}$$

Multiply 2 and 1500 to get 3000.

$$\sqrt{2812500-3000\times 750\left(-\frac{1}{2}\right)}$$

Multiply 3000 and 750 to get 2250000.

$$\sqrt{2812500-2250000\left(-\frac{1}{2}\right)}$$

Express 2250000\left(-\frac{1}{2}\right) as a single fraction.

$$\sqrt{2812500-\frac{2250000\left(-1\right)}{2}}$$

Multiply 2250000 and -1 to get -2250000.

$$\sqrt{2812500-\frac{-2250000}{2}}$$

Divide -2250000 by 2 to get -1125000.

$$\sqrt{2812500-\left(-1125000\right)}$$

The opposite of -1125000 is 1125000.

$$\sqrt{2812500+1125000}$$

Add 2812500 and 1125000 to get 3937500.

$$\sqrt{3937500}$$

Factor 3937500=750^{2}\times 7. Rewrite the square root of the product \sqrt{750^{2}\times 7} as the product of square roots \sqrt{750^{2}}\sqrt{7}. Take the square root of 750^{2}.

$$750\sqrt{7}$$