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What is the simplified form of (√(a^2) * √(b^2))?

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Question: What is the simplified form of (√(a^2) * √(b^2))?

Options:

  1. ab
  2. a^2b^2
  3. a + b
  4. a + b^2

Correct Answer: ab

Solution: 

√(a^2) * √(b^2) = ab.

What is the simplified form of (√(a^2) * √(b^2))?

Practice Questions

Q1
What is the simplified form of (√(a^2) * √(b^2))?
  1. ab
  2. a^2b^2
  3. a + b
  4. a + b^2

Questions & Step-by-Step Solutions

What is the simplified form of (√(a^2) * √(b^2))?
Correct Answer: ab
  • Step 1: Start with the expression √(a^2) * √(b^2).
  • Step 2: Use the property of square roots that states √(x^2) = |x|. So, √(a^2) = |a| and √(b^2) = |b|.
  • Step 3: Substitute |a| and |b| into the expression: |a| * |b|.
  • Step 4: The product |a| * |b| can be simplified to ab if a and b are both positive. Therefore, we write it as ab.
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