Represent the irrational number, sqrt(7) on the numberline.
In order to do this, we need to know what number sqrt(7) is! It's not a nice number either, but we can figure it out.
Some perfect square number that can help us
0 * 0 = 0
1 * 1 = 1
2 * 2 = 4
3 * 3 = 9
4 * 4 = 16
sqrt(7) is asking, what number times itself is 7?
Let's use our perfect square numbers to help.
? * ? = 7
Where does this fit in on our list of perfect square numbers?
2 * 2 = 4
? * ? = 7
3 * 3 = 9
7 lies between 4 and 9! This means that sqrt(7) is somewhere between...
That's right, 2 and 3.
In fact, 7 is closer to 9 (2 away) than 7 is from 4 (3 away). This means, sqrt(7) is closer to 3 than it is to 2 on the numberline.
<-------0 1 2... (sqrt7).. 3 4 5 6 7---->
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Negative square root is -√Square root of negative one is i.
When dealing with real numbers, you cannot take the square root of a negative number. The concept of the imaginary number was created to handle the square root of a negative number.That's almost like saying "when dealing with numbers bigger than 10, you cannot take the square root of 4. If what you are dealing with does not represent a number, then you cannot find its square root.
Mathematicians decided that, since the square root of a negative number does not exist, they would use the first letter of "imaginary" to represent this "value".
The radical symbol ( √ ) followed by a line above what's in the radical, designates positive square root.