Question

\(\sqrt{80}\)

Short answer

The square root of 80 is \(4* \sqrt{5}\)

Step-by-step solution

Prime Factorization

Break down the number 80 into its prime factors. The prime factorization of 80 is \(2^4 * 5\).

Grouping and Simplifying the Factors

Since we are dealing with square roots, we group the factors into pairs. In this case, \(2^4\) can be divided into two groups of 2's: \( (2^2) * (2^2) * 5 \). The square root of \(2^2\) is 2, so it comes out of the square root and the square root of 5 remains inside.

Final Result

So, the final answer is \(2*2* \sqrt{5}\), which equals \(4* \sqrt{5}\)