Solve frac{sqrt{sqrt{16}}-sqrt{6125}}{sqrt{9+16}-sqrt{10-1}}

$$\frac { \sqrt { \sqrt { 16 } } - \sqrt { 6125 } } { \sqrt { 9 + 16 } - \sqrt { 10 - 1 } }$$

Evaluate

$$-\frac{35\sqrt{5}}{2}+1\approx -38.131189606$$

Solution Steps

Calculate the square root of 16 and get 4.

$$\frac{\sqrt{4}-\sqrt{6125}}{\sqrt{9+16}-\sqrt{10-1}}$$

Calculate the square root of 4 and get 2.

$$\frac{2-\sqrt{6125}}{\sqrt{9+16}-\sqrt{10-1}}$$

Factor 6125=35^{2}\times 5. Rewrite the square root of the product \sqrt{35^{2}\times 5} as the product of square roots \sqrt{35^{2}}\sqrt{5}. Take the square root of 35^{2}.

$$\frac{2-35\sqrt{5}}{\sqrt{9+16}-\sqrt{10-1}}$$

Add 9 and 16 to get 25.

$$\frac{2-35\sqrt{5}}{\sqrt{25}-\sqrt{10-1}}$$

Calculate the square root of 25 and get 5.

$$\frac{2-35\sqrt{5}}{5-\sqrt{10-1}}$$

Subtract 1 from 10 to get 9.

$$\frac{2-35\sqrt{5}}{5-\sqrt{9}}$$

Calculate the square root of 9 and get 3.

$$\frac{2-35\sqrt{5}}{5-3}$$

Subtract 3 from 5 to get 2.

$$\frac{2-35\sqrt{5}}{2}$$