Problem 70

Question

Simplify the radical expression. $$ \sqrt{40} $$

Step-by-Step Solution

Verified
Answer
\(\sqrt{40} = 2\sqrt{10}\)
1Step 1: Prime Factorization
Divide 40 into its prime factors. This would be \(2^3 * 5\). So, \( \sqrt{40} = \sqrt{2^3 * 5} \)
2Step 2: Simplify
From the prime factorization, recognize that \(2^2\) is a perfect square. So, extract it out of the root. This simplifies the expression to \(2 * \sqrt{2*5}\)
3Step 3: Final Simplification
Simplify the remaining product in the root, which is \(2*5\), to get 10. So, the final simplification of the square root is \(2 * \sqrt{10}\)