(sqrt 5)/(2 - sqrt 5)
√5/(2-√5) ??
what about it?
If you are rationalizing it, then
= √5/(2-√5) * (2+√5)/(2+√5)
= (2√5 + 5)/(4-5)
= -2√5 - 5
Thanks, but can you please verify how you got the (2√5 + 5)? Because I thought that √5 * (2+√5) would be 2√25.
Just like
3(2x+5) = 6x + 15
just like
3(7+2) = 21 + 6
so is
√5(2+√5)
= 2√5 + √25
= 2√5 + 5
you could also check by evaluating it with your calculator.
To simplify the expression (sqrt 5)/(2 - sqrt 5), we can rationalize the denominator.
Rationalizing the denominator means getting rid of the square root in the denominator by multiplying the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of (2 - sqrt 5) is (2 + sqrt 5).
So, let’s multiply the numerator and denominator by (2 + sqrt 5):
[(sqrt 5) * (2 + sqrt 5)] / [(2 - sqrt 5) * (2 + sqrt 5)]
Expanding the multiplication in the numerator and denominator, we get:
[2sqrt 5 + 5] / [4 - 5]
Simplifying further:
[2sqrt 5 + 5] / [-1]
Finally, we can simplify the expression to:
-2sqrt 5 - 5