This is not a lens about using a calculator to find a square root. This is not a lens about finding a square root to its nearest 10th or 100th or 2 places. This is a lens that helps you get from a large number's square root to a smaller number's square root.

In other words, this will show you how to go from ([square root] 20) to (2 ([square root] 5).

**Reducing Irrational Square Roots**

One of the sorts of problems that shows up on Algebra tests is taking a square root of a number that isn't a perfect square (see a list of all the integers that are perfect squares from 1-625 at the bottom of this lens) and reducing it to an easier to handle version. For example, in the picture here, we start with [square root] 98. But, if you notice when you look at the list, 98 is NOT a perfect square.

98, however, equals 2 X 49. 49 <b>is</b> a perfect square -- it's 7 squared (or 7 X 7). So, as you can see in the second step, [square root] 98 = [square root] 49 X [square root] 2. Or, more succinctly, 7 X [square root] 2.

If the number you are trying to divide is one you don't know (as in you can't tell right away by looking at it what perfect square might be a factor), check out <a href="http://www.squidoo.com/LowCommonDenom">Lowest Common Denominator</a> to see how to break numbers into their factors. Or, if the number is low enough, you can look at the list of squares from 1-625 further down in this lens and work from there.

**Perfect Squares**

This is a list of the first 25 positive integers with their squares.

- 1
- 4
- 4
- 16
- 25
- 36
- 49
- 64
- 81
- 100
- 121
- 144
- 169
- 196
- 225
- 256
- 289
- 324
- 361
- 400
- 441
- 484
- 529
- 576
- 625

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