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How to Estimate Decimals & Square Roots

A key to estimating decimals and square roots is knowing your integer square roots. If you know that two squared equals four, and three cubed equals nine, then if you need to know whether the square root of 7 would be closer to 2 or 3, all you'd have to do is remember your number line and guess 3, because 7 is closer to 9 than 4. However, for a more precise answer, and for larger numbers, there are steps to take to make a more accurate estimate for the square root.

Instructions

- 1
  You can guess a reasonably close solution and divide the square by that guess. For example, let's say that you need the square root of 48. Seven squared is 49, so let's say 6.9 - 48 divided 6.9 equals 6.96.
- 2
  Pick something between your first guess and the answer to Step 1. For the purposes of the example, let's pick 6.93.
- 3
  Divide the original square by this new guess. For the example, 48 divided by 6.93 = 6.926, or about 6.93.
- 4
  Check your estimate against the actual square root, which is 6.928203. If you don't have a calculator, you can still end up with a fairly close estimate in just a few steps.

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