Simplifying Radicals Math Example 2

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

Example 2

medium
Simplify 50x4y3\sqrt{50x^4y^3}.

Solution

  1. 1
    Step 1: 50=25×250 = 25 \times 2; x4=(x2)2x^4 = (x^2)^2; y3=y2⋅yy^3 = y^2 \cdot y.
  2. 2
    Step 2: 50x4y3=25⋅2⋅(x2)2⋅y2⋅y\sqrt{50x^4y^3} = \sqrt{25 \cdot 2 \cdot (x^2)^2 \cdot y^2 \cdot y}.
  3. 3
    Step 3: Extract: 5x2y2y5x^2y\sqrt{2y}.
  4. 4
    Check: (5x2y)2⋅2y=25x4y2⋅2y=50x4y3(5x^2y)^2 \cdot 2y = 25x^4y^2 \cdot 2y = 50x^4y^3 ✓

Answer

5x2y2y5x^2y\sqrt{2y}
With variables, extract even powers from under the radical. Each pair of identical factors comes out as a single factor. Odd exponents leave one factor under the radical.

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 3 medium

Simplify [formula].

Example 4 easy

Simplify [formula].

Example 5 medium

Simplify [formula].

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