Solve (24^2-6^3+sqrt{6}25+5.6*10)^1/2=?

$$( 24 ^ { 2 } - 6 ^ { 3 } + \sqrt { 6 } 25 + 5.6 \times 10 ) ^ { 1 / 2 } = ?$$

Evaluate

$$\sqrt{25\sqrt{6}+416}\approx 21.845760311$$

Solution Steps

Calculate 24 to the power of 2 and get 576.

$$\left(576-6^{3}+25\sqrt{6}+5.6\times 10\right)^{\frac{1}{2}}$$

Calculate 6 to the power of 3 and get 216.

$$\left(576-216+25\sqrt{6}+5.6\times 10\right)^{\frac{1}{2}}$$

Subtract 216 from 576 to get 360.

$$\left(360+25\sqrt{6}+5.6\times 10\right)^{\frac{1}{2}}$$

Multiply 5.6 and 10 to get 56.

$$\left(360+25\sqrt{6}+56\right)^{\frac{1}{2}}$$

Add 360 and 56 to get 416.

$$\left(416+25\sqrt{6}\right)^{\frac{1}{2}}$$