Question

Simplify the radical expression. $$\sqrt{80}$$

Short answer

The simplified form of \( \sqrt{80} \) is \( 4\sqrt{5} \)

Step-by-step solution

Prime Factorization of 80

First, find out the prime factors of 80. The prime factors of 80 are \(2^4 \times 5^1\). So, write the given expression as \( \sqrt {2^4 \times 5} \)

Apply Properties of Radicals

Now, applying the properties of radicals, split the radical into two separate radicals: \( \sqrt{2^4} \times \sqrt{5} \)

Evaluate and Simplify

Solving, \( \sqrt{2^4} = 2^2 = 4 \) and the radical \( \sqrt{5} \) cannot be simplified further. Therefore, the simplified expression becomes \( 4\sqrt{5} \).