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The root function is the inverse operation of the exponentiation.
- With the below exponentiation of the base b to the power of n
<MATH> b^n = a </MATH>
- the base b can be defined back with the root function as:
<MATH> b = \sqrt[n]{a} = a^{\frac{1}{n}} </MATH>
If you need to get the exponent n (power), the operation is not the root function but the logarithm <MATH> n = log_b(a) </MATH>
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Square Root
square root is the inverse of the square operation
- If
<MATH> y^2 = x </MATH>
- then
<MATH> y^{\frac{1}{2}} = \sqrt[2]y = \sqrt{y} = x </MATH>
Every positive number x has two square roots:
- a positive number known as the principal square root and denoted:
- <math>\sqrt {x}</math>
- or <math>x^{\frac{1}{2}}</math> in exponent notation
- a negative number:
- <math>-\sqrt {x}</math>
- or <math>-x^{\frac{1}{2}}</math>
For example: The square roots of 9 are:
- 3 denoted as <math>\sqrt9</math>
- and −3 denoted as <math>-\sqrt9</math>