Question

4) Simplify 4 / √5 − 1 by rationalizing the denominator

Answer 1

multiply numerator and denominator by the "conjugate" of the denominator
\[\frac{4}{\sqrt{5}-1}\times \frac{\sqrt{5}+1}{\sqrt{5}+1}\]

Answer 2

denominator is
\[5-1=4\] because
\[(a+b)(a-b)=a^2-b^2\]

Answer 3

4 root5 + 1 4(root5 + 1) 4(root5 +1)
-------1 x --------- = ---------------- = ------------ = root5 + 1
root5 -1 root5 + 1 (root5)^2 - (1)^2 5 - 1

Answer 4

then in this case you can cancel the 4 but not usually
\[\frac{4(\sqrt{5}+1)}{4}=\sqrt{5+1}\]

Answer 5

final ans is
\[\sqrt{5} + 1\]

and NOT
\[\sqrt{5+1}\]

Answer 6

@satellite

I think by mistake u put the 1 also under the root sign.....