Questions for the Math Heads?

Question

solve:z^(1/2)=5
solve for x: sqrt (x+7)= x+1 i got 2 and -3 is that right
last but not least -5+sqrt(3)/1+sqrt(2)

high school blues can u relate thanks for ne help.

Answer 1

1) z = 25

2) 2 is right, but -3 is not

3) this is not an equation

Answer 2

squaring both sides z=25

b) first you must verify that you are taking the sqrt ofa number >=0

so x+7>=0 x>=-7.Second ,for squaring both sides without introducing wrong solution,both sides must have the same sign.
As sqrt is >=0 x+1>=0 and x>-1

Now squaring both sides we get x+7 = x^2+2x+1 so

x^2 +x-6=0 x= (( -1+- 5))/2 x= 2 and x=-3 BUT as x should be >=-1 x=-3 is NOT a solution

Answer 3

solve:z^(1/2)=5
Square both sides z = 25

solve for x: sqrt (x+7)= x+1 i got 2 and -3 is that right
x+7 =x^2+2x+1
x^2+x-6=0
(x+3)(x-2)
x=-3, x = 2
However you have to check if both are solutions, if you try -3 we don't get a correct solution (square both sides can add extraneous solutions)

last but not least -5+sqrt(3)/1+sqrt(2)
-5+sqrt(3) 1-sqrt(2)
-------------- *---------
1+sqrt(2) (1-sqrt(2))

(-5+sqrt(3)(1-sqrt(2)
------------------------
-1

Answer 4

z^1/2 = 5

That means the square root of z = 5

z^1/2 = 5
(z^1/2)^2 = 5^2
z = 25