How do I find Simplest Radical Form?

Question

How do I find Simplest Radical Form?

For example x^2 + 3x -4 = 0

Answer 1

x^2 +3x -4 = (x+4)(x-1) x=-4, 1, x=sqr1, or -sqr16,

or

x= sqr(x^2+3x-4)= sqr(x^2+3x + 9/4 - 4 - 9/4)

x = sqr((x+3/2)^2 -25/4) = sqr((x+4)(x-1))

or use the quadratic formula:

x = -3/2 + or - (1/2)sqr(9+16) = -3/2 + or - (1/2)(5)= -3/2+5/2 or -3/2-5/2 = -4 or 1

x=-4 or 1

But, not sure exactly what you're asking. Maybe one of the above.

Answer 2

How do I find Simplest Radical Form?

For example x^2 + 3x -4 = 0

You find the solutions and check if they are positive or negative.

factors of -4

-1, 4

-2, 2

The only factors that give 3?

It is -1+ 4.

Plug in for x solutions:

(x-(-1))(x+4)^1/2

If it were x^2+10x+25

1, 25

5,5

(x+5)(x+5)^1/2

This would reduce to (x+5).

So, the simplest forms depend on the trinomial.