Simplifying Radicals Math Example 4

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

Example 4

easy
Simplify 48\sqrt{48}.

Solution

  1. 1
    48=16×348 = 16 \times 3, so 48=43\sqrt{48} = 4\sqrt{3}.
  2. 2
    Check: 42×3=484^2 \times 3 = 48 ✓

Answer

434\sqrt{3}
Factor out the largest perfect square: 48=16×348 = 16 \times 3. Since 16=4\sqrt{16} = 4, the simplified form is 434\sqrt{3}.

About Simplifying Radicals

Simplifying a radical means rewriting it so no perfect-square factor remains under the root sign. For example, √50 = √(25·2) = 5√2. The result — called simplified radical form — has the smallest possible number under the radical.

Learn more about Simplifying Radicals →

More Simplifying Radicals Examples

Example 1 easy

Simplify [formula].

Example 2 medium

Simplify [formula].

Example 3 medium

Simplify [formula].

Example 5 medium

Simplify [formula].

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