How do you find the square root of -300?

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Answer 1 · 2018-03-30T02:05:05

See a solution process below:

First, we can rewrite this expression as:

$sqrt(-300) => sqrt(100 * 3 * -1)$

Next, we can use this rule of radicals to simplify the expression as:

$sqrt(color(red)(a) * color(blue)(b)) = sqrt(color(red)(a)) * sqrt(color(blue)(b))$

$sqrt(color(red)(100) * color(blue)(3) * color(green)(-1)) =>$

$sqrt(color(red)(100)) * sqrt(color(blue)(3)) * sqrt(color(green)(-1)) =>$

$color(red)(10)sqrt(color(blue)(3))sqrt(color(green)(-1)$

The square root of negative 1 is called an imaginary number and can be represented by $i$ .

We can rewrite the expression as:

$color(red)(10)sqrt(color(blue)(3))sqrt(color(green)(-1)) =>$

$color(red)(10)sqrt(color(blue)(3))color(green)(i)$

Or

$color(red)(10)color(green)(i)sqrt(color(blue)(3))$