You are watching: Every positive number has two square roots a

**Why?**

**To know this, we must re iterate the an interpretation of a square root**:

**"The square root of a number is another number, i beg your pardon on multiplying with itself, will offer the initial number."We understand that 10 x 10 = 100**, for this reason 10 is a square source of 100.

**But -10 x -10**is likewise equal come 100, because on multiply two an adverse numbers the result is always a optimistic number.

**Thus both, hopeful 10 and an adverse 10, space square roots of the hopeful number 100.**

### Principle square root

The confident square source of a number is referred to as its principle square root. For example, 10 and also -10 are the two square root of 100, however 10 is called the principle square root.Similarly,the confident number 64 has two square roots, an adverse eight (-8) and also positive eight (+8).36 has actually two square roots, negative six (-6) and also positive six (+6)49 has two square roots, an unfavorable seven (-7) and positive 7 (+7).Generally the positive sign on the left that a number is no written: it is assumed the a number is positive if that does not have a an adverse sign top top its left, so every of the hopeful square root written over may be written without the positive indicators as well. We can conclude that,There are two square roots of a confident number - one square source is positive, vice versa, one square source is negative.**The square source of a number is normally represented by a "+/-**" symbol prior to it as follows:

**Square root of 100 = +/-**√100(where sqrt means symbol that square root)

**Now you need to be wondering about the square root of an adverse numbers**? Do negative numbers have actually two square roots as well? Or other different?

**Negative numbers are not taken right into account in this write-up because they have no real square roots. In simpler words, you deserve to not calculation the square source of a an unfavorable number. This is, because there have the right to not be any positive or an adverse number, i beg your pardon on being multiplied through itself, will give a an adverse result, since positive time positive equals positive**and

**negative times negative equals positive**as well.

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**So the square roots of an unfavorable numbers are called "imaginary numbers**" in math. These are those numbers that do not come under the collection of an unfavorable numbers, hopeful numbers and zero.

**Example: give both the confident and an unfavorable square roots of each number:**

**25**Positive square root = 5Negative square source = -5

**36**Positive square source = 6Negative square source = -6

**49**Positive square root = 7Negative square source = -7

**64**Positive square root = 8Negative square root =-8

**81**Positive square root = 9Negative square root = -9

**100**Positive square source = 10Negative square root = -10

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6 comments:

Kasyaf SufiSeptember 12, 2013 at 7:46 PM

how about questions below?1) the square roots of 25 are:2) the square root of 5^2 are:3) the square root of (-5)^2 are:4) sqt 5^2 is 5 and -5, is it correct?