Math Problem Statement

12 square root 8x + 2x square root 4x

Solution

The given expression is:

128x+2x4x12 \sqrt{8x} + 2x \sqrt{4x}

Step 1: Simplify the square roots.

We can express 8x\sqrt{8x} and 4x\sqrt{4x} as:

8x=4×2x=4×2x=22x\sqrt{8x} = \sqrt{4 \times 2x} = \sqrt{4} \times \sqrt{2x} = 2\sqrt{2x} 4x=4×x=2x\sqrt{4x} = \sqrt{4} \times \sqrt{x} = 2\sqrt{x}

Step 2: Substitute the simplified square roots back into the expression.

128x=12×22x=242x12 \sqrt{8x} = 12 \times 2 \sqrt{2x} = 24 \sqrt{2x} 2x4x=2x×2x=4xx2x \sqrt{4x} = 2x \times 2 \sqrt{x} = 4x \sqrt{x}

Step 3: Combine the terms.

Now substitute both simplified terms into the original expression:

242x+4xx24 \sqrt{2x} + 4x \sqrt{x}

Thus, the simplified expression is:

242x+4xx24 \sqrt{2x} + 4x \sqrt{x}

Let me know if you'd like more details, or if you have any questions!

Here are some related problems for practice:

  1. Simplify 1018x+3x9x10 \sqrt{18x} + 3x \sqrt{9x}.
  2. Solve 156x5x3x15 \sqrt{6x} - 5x \sqrt{3x}.
  3. Simplify 750x+5x25x7 \sqrt{50x} + 5x \sqrt{25x}.
  4. Expand 8x16x+2x64x8x \sqrt{16x} + 2x \sqrt{64x}.
  5. Factor 432x+6x2x4 \sqrt{32x} + 6x \sqrt{2x}.

Tip: Always simplify square roots by breaking them down into perfect squares before simplifying the overall expression.

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Math Problem Analysis

Mathematical Concepts

Algebra
Simplification of Radicals
Square Roots

Formulas

√(a * b) = √a * √b

Theorems

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Suitable Grade Level

Grades 9-11