How do I simplify square root 48 + square root 27?

To simplify the expression √48 + √27, we can break down each square root into its prime factors.

Step 1: Factor the Numbers

First, let's factor 48 and 27:

• 48 = 16 × 3 = 4² × 3
• 27 = 9 × 3 = 3² × 3

Step 2: Simplify Each Square Root

Now, we can simplify the square roots:

• √48 = √(16 × 3) = √16 × √3 = 4√3
• √27 = √(9 × 3) = √9 × √3 = 3√3

Step 3: Combine Like Terms

Now that we have simplified both square roots, we can combine them:

4√3 + 3√3 = (4 + 3)√3 = 7√3

Final Result

The simplified form of √48 + √27 is 7√3.