# How do you write the given expression terms of i: sqrt(-45)?

Mar 3, 2018

the special symbol i is used to represent the square root of negative 1, $\sqrt{-} 1$

#### Explanation:

We know there is no such thing in the real number universe as the $\sqrt{-} 1$ because there are no two identical numbers that we can multiply together to get -1 as our answer.

11 = 1 and -1-1 is also 1. Obviously 1*-1 = -1, but 1 and -1 are not the same number. They both have the same magnitude (distance from zero), but they are not identical.

So, when we have a number that involves a negative square root, math developed a plan to get around that problem by saying that anytime we run across that issue, we make our number positive so we can deal with it and put an i at the end.

So, in your case $\sqrt{-} 45 \to \sqrt{45} i$

Note that since 45 = 9*5, your answer can be simplified to:

$\sqrt{45} i \to \sqrt{9 \cdot 5} i \to 3 \sqrt{5} i$