Question

[tex]evaluate after rationalising the denominator of (25/ \sqrt{40} - \sqrt{80})
[/tex]

Answer 1

25/(√40 - √80)

25(√40 +√80)/(√40 -√80)( √40 +√80)

25(√40 +√80)/(40 -80)

25(2√10 + 4√5)/( -40)

5( 2√10 + 4√5)/(-8)

5( √10 + 2√5)/(-4)

( 5√10 + 10√5)/( -4)

Answer 2

25/(√40 - √80)
= 25/[√40 ( 1-√2)]
=25/[2√10(1-√2)]

= [25 * (1+√2)]/[2√10(1-√2)(1+√2)]

=[25 *√10 (1+√2)]/[2√10*√10 (1-2)]

=[25√10 (1+√2)]/[-20]

= 5√10(1+√2)/(-4)