Solve (sqrt{12^{2}+9^{2}}-sqrt{25^{2}-15^2})^2:(-sqrt{3^2+4^2})

$$( \sqrt { 12 ^ { 2 } + 9 ^ { 2 } } - \sqrt { 25 ^ { 2 } - 15 ^ { 2 } } ) ^ { 2 } : ( - \sqrt { 3 ^ { 2 } + 4 ^ { 2 } } )$$

Evaluate

$$-5$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$\frac{\left(\sqrt{144+9^{2}}-\sqrt{25^{2}-15^{2}}\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{\left(\sqrt{144+81}-\sqrt{25^{2}-15^{2}}\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Add 144 and 81 to get 225.

$$\frac{\left(\sqrt{225}-\sqrt{25^{2}-15^{2}}\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Calculate the square root of 225 and get 15.

$$\frac{\left(15-\sqrt{25^{2}-15^{2}}\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{\left(15-\sqrt{625-15^{2}}\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{\left(15-\sqrt{625-225}\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Subtract 225 from 625 to get 400.

$$\frac{\left(15-\sqrt{400}\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Calculate the square root of 400 and get 20.

$$\frac{\left(15-20\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Subtract 20 from 15 to get -5.

$$\frac{\left(-5\right)^{2}}{-\sqrt{3^{2}+4^{2}}}$$

Calculate -5 to the power of 2 and get 25.

$$\frac{25}{-\sqrt{3^{2}+4^{2}}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{25}{-\sqrt{9+4^{2}}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{25}{-\sqrt{9+16}}$$

Add 9 and 16 to get 25.

$$\frac{25}{-\sqrt{25}}$$

Calculate the square root of 25 and get 5.

$$\frac{25}{-5}$$

Divide 25 by -5 to get -5.

$$-5$$

Factor

$$-5$$