When comparing square roots is the one that is higher automatically bigger?

Answer 1

The answer depends on what you mean by higher.

81 is bigger than 64.

But the square roots of 81 are -9 and +9 while the square roots of 64 are -8 and +8.

You then have

-9 < -8 so sqrt(81) < sqrt(64)

-9 < 8 so sqrt(81) < sqrt(64)

-8 < 9 so sqrt(64) < sqrt(81)

8 < 9 so sqrt(64) < sqrt(81)

Take your pick!