Question

State whether the following are true or false.

The square roots of 36 are + and - 6. I wrote down false for this cause I thought it was only + 6, but the real answer is true, and I want to know that how can it be negative?

Also for this:

Convert the following radicals to mixed radicals in simplest form.

I did this without making the factor tree, my teacher showed me an easy way.

ã50 = ã2*5*5 = 5*5ã2 = 25ã2
That's what I got 25ã2, but the answer is supposed to be 5ã2. I don't understand, did they reduce or something?

Answer 1

Sorry this ã was supposed to be the radical sign, don't know why it never showed up.

Answer 2

A bit of a technicality here.
The √ symbol is defined as the principal square root, which means, the positive square root of a number
Thus √36 = +6

on the other hand if you have
x^2 = 16
then ±x = √16 = 4 from which we get
x = ± 4

so the -4 actually does not come from √16 but rather from
x^2 = 16

Your question is a poor choice for a true or false type question.

2nd part of your post:

√50 = √25√2 = 5√2