why squareroot of100 is not equal to plus or minus square root of (-10*-10)?

Answer 1

There is a difference between stating the solutions of the equation x² = 100 and stating the square root of 100. In the equation, you are asking yourself, "what number(s) squared equal 100?" There are two answers to that question, +10 and -10. But sqrt 100 is 10, while -sqrt 100 is -10. We call sqrt of 100 the primary square root and that is the positive unless otherwise indicated.

Answer 2

When you have a multiplication of roots, you can split it up so that each is it's own root. (try it with root (2*2) to convince yourself) So, for example, in this situation when you split up the roots, root(-10*-10)= root(-10)*root(-10). As you can see, the number under the roots in both of these is a negative, which is undefined: you can't take the square root of a number less than 0.
So, even though-10*-10 does equal +100, it is not mathematically correct to express root (100) this way.
Hope that helps!

Answer 3

Mathematical convention - square roots are always positive numbers (simpler to express).

Answer 4

Mainly because the +/- should be OUTSIDE the radical and not inside.