Question

Simplify the radical expression. $$\sqrt{50}$$

Short answer

The simplified radical expression of \(\sqrt{50}\) is \(5\sqrt{2}\).

Step-by-step solution

Prime Factorization of Number

Decompose the number 50 into its prime factors. The prime factorization of 50 is \(2 \times 5 \times 5\) or \(2 \times 5^2\).

Pairing the Prime Factors

Pair up the prime factors. In this case \(5^2\) makes a pair.

Simplifying the Expression

Take out the pairs from under the square root. For each pair, one number can come out from under the radical as it makes a square. So, the number \(5\) comes out and the number \(2\) left under the radical because it's not part of a pair. So the square root becomes \(5\sqrt{2}\).