Question

How do you simplify: square root of 300 divided by the square root of 6?

Answer 1

square root of 300 divided by the square root of 6 `= +-5sqrt(2)`

Explanation:

(Assuming your use of the phrase "square root" is intended to include both positive and negative roots... as opposed to the symbol `sqrt("something")` which is defined to be only the positive roots):

Since `sqrt(a/b) = sqrt(a)/sqrt(b)`

`+- sqrt(300)/sqrt(6) = +- sqrt(50)`

`color(white)("XXXX")` `= +- sqrt(5^2*2)`

`color(white)("XXXX")` `= +- sqrt(5^2)*sqrt(2)`

`color(white)("XXXX")` `= +- 5sqrt(2)`