Solve frac{3-sqrt{4001^2-7}}{4*001-4}=

$$\frac { 3 - \sqrt { 4001 ^ { 2 } - 7 } } { 4 \cdot 001 - 4 } =$$

Evaluate

$$\frac{3\left(\sqrt{1778666}-1\right)}{4}\approx 999.499781305$$

Solution Steps

Calculate 4001 to the power of 2 and get 16008001.

$$\frac{3-\sqrt{16008001-7}}{4\times 0\times 0\times 1-4}$$

Subtract 7 from 16008001 to get 16007994.

$$\frac{3-\sqrt{16007994}}{4\times 0\times 0\times 1-4}$$

Factor 16007994=3^{2}\times 1778666. Rewrite the square root of the product \sqrt{3^{2}\times 1778666} as the product of square roots \sqrt{3^{2}}\sqrt{1778666}. Take the square root of 3^{2}.

$$\frac{3-3\sqrt{1778666}}{4\times 0\times 0\times 1-4}$$

Multiply 4 and 0 to get 0.

$$\frac{3-3\sqrt{1778666}}{0\times 0\times 1-4}$$

Multiply 0 and 0 to get 0.

$$\frac{3-3\sqrt{1778666}}{0\times 1-4}$$

Multiply 0 and 1 to get 0.

$$\frac{3-3\sqrt{1778666}}{0-4}$$

Subtract 4 from 0 to get -4.

$$\frac{3-3\sqrt{1778666}}{-4}$$