Solve sqrt{{left(3sqrt{41}right)}^2-15^2}

$$\sqrt{ { \left(3 \sqrt{ 41 } \right) }^{ 2 } - { 15 }^{ 2 } }$$

Evaluate

$$12$$

Solution Steps

Expand \left(3\sqrt{41}\right)^{2}.

$$\sqrt{3^{2}\left(\sqrt{41}\right)^{2}-15^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt{9\left(\sqrt{41}\right)^{2}-15^{2}}$$

The square of \sqrt{41} is 41.

$$\sqrt{9\times 41-15^{2}}$$

Multiply 9 and 41 to get 369.

$$\sqrt{369-15^{2}}$$

Calculate 15 to the power of 2 and get 225.

$$\sqrt{369-225}$$

Subtract 225 from 369 to get 144.

$$\sqrt{144}$$

Calculate the square root of 144 and get 12.

$$12$$

Factor

$$2^{2}\times 3$$