evaluate expression
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\(\displaystyle \sqrt{-9}\)
Have you learned that this expression has no meaning, in the Real number system?
In other words, we cannot take the square root of a negative number, within the Real number system.
In order to take the square root of a negative number, we need to enter the realm of Complex numbers with an imaginary part.
I mean, we need to use the imaginary unit \(\displaystyle i\).
Have you learned the definition of the imaginary unit \(\displaystyle i\) ?
\(\displaystyle i \ = \ \sqrt{-1}\)
Here's an example, using the properties of radicals to separate the factor of -1 and simplify the radical.
\(\displaystyle \sqrt{-144}\)
\(\displaystyle \sqrt{(144)(-1)}\)
\(\displaystyle \sqrt{144} \cdot \sqrt{-1}\)
\(\displaystyle \sqrt{144} \cdot i\)
\(\displaystyle 12 \ i\)
Questions?
\(\displaystyle \sqrt{-9}\)
Have you learned that this expression has no meaning, in the Real number system?
In other words, we cannot take the square root of a negative number, within the Real number system.
In order to take the square root of a negative number, we need to enter the realm of Complex numbers with an imaginary part.
I mean, we need to use the imaginary unit \(\displaystyle i\).
Have you learned the definition of the imaginary unit \(\displaystyle i\) ?
\(\displaystyle i \ = \ \sqrt{-1}\)
Here's an example, using the properties of radicals to separate the factor of -1 and simplify the radical.
\(\displaystyle \sqrt{-144}\)
\(\displaystyle \sqrt{(144)(-1)}\)
\(\displaystyle \sqrt{144} \cdot \sqrt{-1}\)
\(\displaystyle \sqrt{144} \cdot i\)
\(\displaystyle 12 \ i\)
Questions?