Question

Express 1/ root 5 +root 3-root 8 with rational denominators

Answer 1

Hi ,

1/( √5 + √3 - √8 )

=(√5+√3+√8)/[(√5+√3-√8)(√5+√3+√8)]

= (√5+√3+√8)/{[(√5+√3)-√8][(√5+√3)-√8]}

= (√5+√3+√8)/[( √5 + √3 )² - ( √8 )² ]

= ( √5+√3+√8 )/[(√5)²+(√3)²+2(√5)(√3) - 8 ]

= ( √5 + √3 + √8 )/[ 5 + 3 +2√15 - 8 ]

= ( √5 + √3 + √8 )/2√15

=[ (√3 +√5 + √8 ) × √15 ]/[ 2√15×√15]

= ( 3√5 + 5√3 + √120 )/30

I hope this helps you.

: )

Answer 2

Answer:

$\sqrt{5 + \sqrt{3 + \sqrt{8 \\ } }$