Question

rationalize the denominator of 4/5+the sq root of 2

Answer 1

\[\frac{4}{5+\sqrt2}\]?

Answer 2

rationalize by multiplying the numerator and denominator by the conjugate of the denominator
the conjugate of \(a+\sqrt b\) is \(a-\sqrt b\) and this works because
\[(a+\sqrt b)(a-\sqrt b)=a^2-b\] a number with no radical

Answer 3

in your example it is
\[\frac{4}{5+\sqrt2}\times \frac{5-\sqrt 2}{5-\sqrt2}\]
\[=\frac{4(5-\sqrt 2)}{5^2-2}\] and you can clean it up a little after that

Answer 4

thank you! i get it now

Answer 5

also i keep getting the wrong answer on this:
(7+sq root of 2)(8- 3 sq root 2)