Problem 63 - Algebra 1: Concepts and Skills

Question

Simplify the radical expression. $$\sqrt{60}$$

Step-by-Step Solution

Answer

The simplified radical expression of \(\sqrt{60}\) is \(2\sqrt{15}\).

Step 1: Express as prime factors

Firstly, express the number under the square root as a product of its prime factors. The prime factorization of 60 can be carried out by dividing it repeatedly by prime numbers. The result for 60 is \(2^2 \cdot 3 \cdot 5\). So we can express the given radical expression as \(\sqrt{60} = \sqrt{2^2 \cdot 3 \cdot 5}\)

Step 2: Apply the rules of square roots

By applying the rules of square roots, pairs of identical factors under the radical can be taken out. In this case, \(2^2\) can come out since a perfect square is present. This results in \(2\sqrt{3 \cdot 5}\).

Step 3: Final expression

Now, multiply the numbers under the radical to obtain the final simplified expression, which is \(2\sqrt{15}\).