Question

racionalize: a) 4/√3 b)√2/√5 c)2√3/√2 d)3/√2+1

Answer 1

a)
$\frac{4}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } = \frac{4 \sqrt{3} }{3}$
b)
$\frac{ \sqrt{2} }{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } = \frac{ \sqrt{10} }{5}$

Answer 2

a) 4 / √3 = 4 . √3 / √3 . √3 = 4.√3 / √9 = (4 . √3 ) / 3 
b)√2 / √5 = √2 . √5 / √5 . √5 = √2 . √5 / √25 = √10 / 5
c)2.√3 / √2 = 2.√3 . √2  /  √2 . √2 = 2.√6 / √4 = 2.√6 / 2 = √6
d)3 / √2 + 1 = 3 (√2 - 1 )  / (√2 + 1 ) (√2 - 1 ) = 3(√2 - 1 ) / √4 - √2 + √2 - 1 = 
= 3 (√2 - 1 ) / 2 - 1  = 3 (√2 - 1 )  /  1 = 3 (√2 - 1 )