can you help me solve these?

Question

1.) - √-25

2.) (- √-25) ^2

Answer 1

PROBLEM 1:

- √(-25)

- √(25)(-1)

- [ √(25) * √(-1) ]

- [ 5 * i ]

Answer:
-5i

PROBLEM 2:
(- √(-25))²

You already know that the part inside the parentheses is -5i

(-5i)²

= (-5)²(i)²

= 25 x -1

Answer:
-25

You can also solve this just by thinking logically. You have the square of a negative number. This is the same as the square of the positive number:

(-√-25)² --> (√-25)²

And the square of a square root is just the number itself.

Answer:
-25

Answer 2

The square root of a negative number gives you the imaginary number i with the root.
1) sqrt(25) = 5. So, sqrt(-25)=5i.
Therefore, -sqrt(-25)=-5i

2) Take your answer from #1 (-5i) and square it:
(-5i)^2=25i^2
i^2=-1, so 25i^2=25(-1)
=-25

Answer 3

you need to know about complex numbers for this

1) sqrt ( - 25 ) = sqrt (-1 * 25 ) = 5 * sqrt (-1)

In complex numbers one writes sqrt (-1) as i [ or j if you are an electrical engineer ] so

- sqrt ( -25 ) = -5 i

2) ( -5 i )^2 = (-5)^2 * (i)^2 = 25 * (-1) = - 25

Answer 4

Radicals can be factored:

-√(-25) = -√(25)√(-1)
= -5√(-1)
= -5i

(-√-25)² = (√-25)²
= [√((-1)(25))]²
= [√(-1)√(25)]²
= [√(-1)]² [√(25)]²
= [i]² [5]²
= -25

Answer 5

[06]
1)-sqrt(-25)
= - sqrt(25*-1)
= -sqrt(25*i^2)
=-5i
=
2)(-sqrt(-25)^2
=(-5i)^2
=25i^2
=-25

Answer 6

-5i

-5