Simplify. assume that all variables are non negitive-√40 , √25x-25, √y^9?

Answer 1

Is the hyphen a negation of √40, or an indication that the problems follow? If the former, negate my first answer.

√40 =
√(4*10) =
√4*√10 =
2√10

For the second one, assuming it's all under the same radical:

√(25x-25) =
√(25 (x-1)) =
√25 * √(x - 1) =
5√(x-1)

√y^9 =
√(y^2 * y^2 * y^2 * y^2 * y) =
√(y^2) * √(y^2) * √(y^2) * √(y^2) * √y =
y * y * y * y * √y =
y^4 √y

The one theme that's repeated several times above is that √(ab) = √a * √b. You can break perfect squares out into their own square root and simplify that part.

And the final one could be shorter if I used the fact that √(a^b) = a^(b/2) (i.e., taking a square root of a power, divides the exponent by two).

Answer 2

1)
-√40=-√(4*10) =- 2√10

2)
√(25x-25)=√(25x-25)
=√(25 (x-1))
= √25 √(x - 1)
= 5√(x-1)
OR
√25x-25= 5 X -25 = -125
OR
√(25x-25) = √(-625) = 25 i

3)
√y^9 = √[(y^4)^2*y^1]=y^4√y

QED