517√− 4
is rationalized by multiplying the numerator and denominator by what?
To rationalize the expression 517√− 4, we need to eliminate the radical in the denominator.
We can do this by multiplying both the numerator and denominator by the conjugate of the denominator, which is 517√+ 4.
(517√− 4) * (517√+ 4) / (517√+ 4)
Simplifying this expression, we get:
(517√)^2 - 4^2 / (517√)^2 - 4^2
= 267089 - 16 / 267089 + 16
= 267073 / 267105
Therefore, multiplying the numerator and denominator by 517√+ 4 rationalizes the expression 517√− 4.
To rationalize the expression 517√− 4, we can multiply the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of √− 4 is √− 4 itself.
So, we multiply the numerator and denominator by √− 4:
(517√− 4) * (√− 4) / (√− 4)
Simplifying this expression gives:
517√(-4) * √(-4) / √(-4) * √(-4)
= 517 * (−4) / −4 * −4
= −2068 / 16
= -129.25
Rationalizing the expression by multiplying the numerator and denominator by √− 4 gives us the rationalized form of the expression: -129.25.