Squareroots negative answers

GRE Quant Problem Solving
1

The ratio of 16 to g is equal to the ratio of g to 49.

Quantity A
g

Quantity B
28

Greg mentioned in his class that you do not consider negative roots for the GRE. But the solution in Manhattan considered it and gave the answer D. Won’t it be C considering we do not factor in the negative roots?

2

In this question, when g^2 = 784, the solutions are:

  • g = \sqrt{784}
  • g = -\sqrt{784}

What this is means is that:

\sqrt{784} is always equal to |28| which is the same as positive 28. But when you put the - sign in front of it, you can make it negative again.

So our two solutions in this case are:

  • g = |28|
  • g = -|28|

So this becomes 28 and -28. Does that make sense?

3

not really :stuck_out_tongue:

4

\sqrt{16} is always equal to 4. It’s not the same as \pm4.

But if you say x^2=16, then x can be:

  • \sqrt{16} which is 4
  • -\sqrt{16} which is -4

But notice in both examples above \sqrt{16} itself is always positive 4.