Radical Operations Math Example 1

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

Example 1

easy
Simplify 35+753\sqrt{5} + 7\sqrt{5}.

Solution

  1. 1
    Step 1: Both terms have the same radicand 5\sqrt{5}, so they are like radicals.
  2. 2
    Step 2: Add coefficients: (3+7)5=105(3 + 7)\sqrt{5} = 10\sqrt{5}.
  3. 3
    Check: Think of 5\sqrt{5} as a variable: 3a+7a=10a3a + 7a = 10a ✓

Answer

10510\sqrt{5}
Like radicals (same radicand and same index) can be combined by adding or subtracting their coefficients, just like combining like terms in algebra.

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 2 medium

Simplify [formula].

Example 3 medium

Multiply [formula] and simplify.

Example 4 hard

Expand and simplify [formula].

← All Radical Operations Examples Radical Operations Concept