Radical Operations Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Simplify 12+27\sqrt{12} + \sqrt{27}.

Solution

  1. 1
    Step 1: Simplify each radical: 12=23\sqrt{12} = 2\sqrt{3} and 27=33\sqrt{27} = 3\sqrt{3}.
  2. 2
    Step 2: Now they have the same radicand: 23+33=532\sqrt{3} + 3\sqrt{3} = 5\sqrt{3}.
  3. 3
    Check: 12≈3.46\sqrt{12} \approx 3.46, 27≈5.20\sqrt{27} \approx 5.20, sum ≈8.66\approx 8.66; 53≈8.665\sqrt{3} \approx 8.66 ✓

Answer

535\sqrt{3}
Radicals that look unlike may become like radicals after simplifying. Always simplify radicals first before attempting to add or subtract them.

About Radical Operations

Adding, subtracting, and multiplying expressions that contain radicals. Like terms (same radicand) can be combined for addition and subtraction; for multiplication, use a⋅b=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{ab}.

Learn more about Radical Operations →

More Radical Operations Examples

Example 1 easy

Simplify [formula].

Example 3 medium

Multiply [formula] and simplify.

Example 4 hard

Expand and simplify [formula].

← All Radical Operations Examples Radical Operations Concept