Solve sqrt{(5sqrt{2})^2-5}

$$\sqrt { ( 5 \sqrt { 2 } ) ^ { 2 } - 5 }$$

Evaluate

$$3\sqrt{5}\approx 6.708203932$$

Solution Steps

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

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

Calculate 5 to the power of 2 and get 25.

$$\sqrt{25\left(\sqrt{2}\right)^{2}-5}$$

The square of \sqrt{2} is 2.

$$\sqrt{25\times 2-5}$$

Multiply 25 and 2 to get 50.

$$\sqrt{50-5}$$

Subtract 5 from 50 to get 45.

$$\sqrt{45}$$

Factor 45=3^{2}\times 5. Rewrite the square root of the product \sqrt{3^{2}\times 5} as the product of square roots \sqrt{3^{2}}\sqrt{5}. Take the square root of 3^{2}.

$$3\sqrt{5}$$