Problem 73

Question

Simplify the radical expression. $$ \sqrt{200} $$

Step-by-Step Solution

Verified
Answer
The simplified form of \(\sqrt{200}\) is \(10\sqrt{2}\).
1Step 1: Prime Factorize The Number Under The Radical
We need to start by finding the prime factorization of 200. The prime factors of 200 are 2, 2, 2, 5, 5. We can group them into pairs, this gives us two pairs (2,2) and (5,5) and a lone 2.
2Step 2: Simplify The Radical Expression
For each pair of identical factors, remove one number from the pair out of the root. The pair (2,2) becomes 2 and the pair (5,5) becomes 5. The remaining lone 2 stays within the square root. This simplification gives us: \(2*5*\sqrt{2} = 10\sqrt{2}\)