Solve sqrt{10^2-{left(5sqrt{3}right)}^2}

$$\sqrt{ { 10 }^{ 2 } - { \left(5 \sqrt{ 3 } \right) }^{ 2 } }$$

Evaluate

$$5$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\sqrt{100-\left(5\sqrt{3}\right)^{2}}$$

Expand \left(5\sqrt{3}\right)^{2}.

$$\sqrt{100-5^{2}\left(\sqrt{3}\right)^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\sqrt{100-25\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$\sqrt{100-25\times 3}$$

Multiply 25 and 3 to get 75.

$$\sqrt{100-75}$$

Subtract 75 from 100 to get 25.

$$\sqrt{25}$$

Calculate the square root of 25 and get 5.

$$5$$

Factor

$$5$$