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move up our only "math book" reference to the first paragraph
The '''square root''' of a number ''x'' is a number that, multiplied by itself, results in ''x''. For example, 5 × 5 = 25 so 5 is a square root of 25. Also, -5 × -5 = 25 so 5 is the other square root.
The '''square root''' of a number ''x'' is a number that, multiplied by itself, results in ''x''.<ref>"Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3)<sup>2</sup> = (+3)<sup>2</sup> = 9." [http://mathworld.wolfram.com/SquareRoot.html Wolfram Research] - Eric Weisstein </ref> For example, 5 × 5 = 25 so 5 is a square root of 25. Also, -5 × -5 = 25 so 5 is the other square root.
The positive square root is the length of one side of a square. Multiply the length by itself, and the product is the area of the square.
The positive square root is the length of one side of a square. Multiply the length by itself, and the product is the area of the square.
<math>x^2\ = y</math> implies <math>|x| = \sqrt{y}</math>
<math>x^2\ = y</math> implies <math>|x| = \sqrt{y}</math>
This shows that all numbers other than zero have two square roots, one positive and one negative: <ref>"Note that any positive real number has two square roots, one positive and one negative. For example, the square roots of 9 are -3 and +3, since (-3)<sup>2</sup> = (+3)<sup>2</sup> = 9." [http://mathworld.wolfram.com/SquareRoot.html Wolfram Research] - Eric Weisstein </ref>
This shows that all numbers other than zero have two square roots, one positive and one negative:
:<math>3 \cdot 3 = 9</math> and <math>-3 \cdot -3 = 9</math>
:<math>3 \cdot 3 = 9</math> and <math>-3 \cdot -3 = 9</math>