Problem 72 - Algebra 1: Concepts and Skills

Question

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

Step-by-Step Solution

Answer

The radical expression \(\sqrt{60}\) simplifies to \(6\sqrt{5}\).

Step 1: Identify Largest Perfect Square

Start by identifying the largest perfect square that divides into 60. The perfect squares that are less than or equal to 60 are: 1, 4, 9, 16, 25, 36, 49. Out of these, the largest perfect square, that divides into 60, is 36.

Step 2: Express the Given Number as a Product

The number 60 can be expressed as the product of two factors, one of which is the largest perfect square identified in step 1. \n Hence, \(60 = 36 \times 5\). We will use this to simplify the radical expression.

Step 3: Apply the Property of Radicals

The square root of a product is the product of the square roots of the multiplicands. This property of radicals can be applied here to simplify the radical expression. \n So, \(\sqrt{60}\) can be written as \(\sqrt{36 \times 5} = \sqrt{36} \times \sqrt{5}\)

Step 4: Simplify the Radical Expression

Now simplify the radical expression. The square root of 36 is 6, so the expression becomes \(6\sqrt{5}\).