Question

Pls help rationalize

Answer 1

See answers below.

Explanation:

All of these use the same idea: multiply numerator and denominator by the conjugate radical (an identical expression but with the sign between terms changed).

`(1)/(13-√(15))\cdot(13+√(15))/(13+√(15))=(13+√(15))/(169-15)}\\\\=(13+√(15))/(154)`

`(1)/(√(13)-√(11)) \cdot (√(13)+√(11))/(√(13)+√(11))=(√(13)+√(11))/(13-11)\\\\=(√(13)+√(11))/(2)`

`(1)/(√(21)+√(29))\cdot(√(21)+√(29))/(√(21)+√(29))=(√(21)+√(29))/(21-29)\\\\=(√(21)+√(29))/(-8)`

Note: Here's an example of what happens when you multiply conjugate radicals.

`(√(13)-√(11)})(√(13)+√(11))=13-√(11)√(13)+√(13)√(11)-11=13-11`

When you FOIL those binomials, the square roots go away!

Answer 2

1= 0.109

2= 3.46

3 = -(minus)1.24

Step-by-step explanation: