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What is the simplified form of (√(2) * √(8))?

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Question: What is the simplified form of (√(2) * √(8))?

Options:

  1. √(16)
  2. 4
  3. 2√(2)
  4. 8

Correct Answer: 2√(2)

Solution: 

√(2) * √(8) = √(16) = 4, but simplified is 2√(2).

What is the simplified form of (√(2) * √(8))?

Practice Questions

Q1
What is the simplified form of (√(2) * √(8))?
  1. √(16)
  2. 4
  3. 2√(2)
  4. 8

Questions & Step-by-Step Solutions

What is the simplified form of (√(2) * √(8))?
Correct Answer: 2√(2)
  • Step 1: Start with the expression √(2) * √(8).
  • Step 2: Use the property of square roots that says √(a) * √(b) = √(a * b).
  • Step 3: Apply this property: √(2) * √(8) = √(2 * 8).
  • Step 4: Calculate 2 * 8, which equals 16.
  • Step 5: Now we have √(16).
  • Step 6: Find the square root of 16, which is 4.
  • Step 7: However, we want the simplified form, so we go back to √(2) * √(8).
  • Step 8: Rewrite √(8) as √(4 * 2).
  • Step 9: Use the property again: √(4 * 2) = √(4) * √(2).
  • Step 10: Calculate √(4), which is 2.
  • Step 11: Now we have √(2) * 2 = 2√(2).
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