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Square roots
Positive and negative square roots
Every positive number has two square roots, one positive and the other negative.

 32=9 so 3 is a square root of 9 (-3)2=9 so -3 is also a square root of 9

In general, every positive number has two square roots. However, a negative number does not have any square roots in the real number system. For example, the number -16 has no square roots because it is imposible to find a real number that when squared gives negative 16. When you square any real number, whether it is positive, negative, or 0, the result cannot be negative.

Remember that the square root symbol means the positive square root. There is an invisible + sign in front of the radical. Although it is invisible, it is very important.

For example,

• When we mean to indicate the positive square root, we write $\sqrt{9}=3$
• When we mean to indicate the negative square root, we write $-\sqrt{9}=-3$
• When we mean to indicate the positive and negative square roots, we write $\pm\sqrt{9}=\pm\;3$ .