Radical Operations Math Example 3

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

Example 3

medium
Multiply 6⋅10\sqrt{6} \cdot \sqrt{10} and simplify.

Solution

  1. 1
    6⋅10=60=4⋅15=215\sqrt{6} \cdot \sqrt{10} = \sqrt{60} = \sqrt{4 \cdot 15} = 2\sqrt{15}.
  2. 2
    Check: 6×10=606 \times 10 = 60 and (2)2×15=60(2)^2 \times 15 = 60 ✓

Answer

2152\sqrt{15}
The product rule a⋅b=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{ab} combines the radicands. Then simplify the result by extracting any perfect square factors.

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 2 medium

Simplify [formula].

Example 4 hard

Expand and simplify [formula].

← All Radical Operations Examples Radical Operations Concept