Simplifying roots, step by step

√(64x²) is 8x, and the tempting wrong answers each take half of it out and leave the other half behind.

The question

Check this line: √(96x²) + √(6x²) = 5x. Which is correct?

Check this line: √(96x²) + √(6x²) = 5x. Which is correct?

√(96x²) + √(6x²)
√(96x²) + √(6x²)=4x√6 + x√6
√(96x²) + √(6x²)=4x√6 + x√6
√(96x²) + √(6x²)=5x√6
√(96x²) + √(6x²)=5x√6
they wrote:5x
  1. Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.
  2. On your own, and writing the step nobody writes down: √(96x²) + √(6x²) becomes 4x√6 + x√6.
  3. Tidy that up and it is 5x√6.
  4. Now compare. They wrote 5x, and the part that would not come out was dropped — so the correct answer is 5x√6.

How it works.

  1. 01

    Do not check by reading their line. Somebody else's working is the most persuasive thing on the page, and rereading it is how you end up agreeing with it — do the step yourself first, then compare.

  2. 02

    On your own, and writing the step nobody writes down: √(96x²) + √(6x²) becomes 4x√6 + x√6.

  3. 03

    Tidy that up and it is 5x√6.

  4. 04

    Now compare. They wrote 5x, and the part that would not come out was dropped — so the correct answer is 5x√6.