help simplfy expressions

Question

Please help simplify these expressions:

 

1.  √a + √b

     √a - √b

 

 

2.  √5 + 1

     √5 - 1

 

 

3.  3√2 - 2√3

 

 

4.  √3(√6 - 2√3)

 

5.  √18 - √3

        √6

 

 

thanks

Answer 1

1. (√a+√b)/(√a–√b)

 

= (√a+√b)^2/((√a+√b)(√a–√b))

 

= (a + 2√(ab) + b)/(a–b)


2. Same technique as for 1.

3. 3√2 - 2√3

 

No simplification possible.


4. √3(√6 - 2√3)

 

= √3(√2 √3 - 2√3)

 

= √3√3(√2 - 2)

 

= 3(√2 - 2)


5. (√18 - √3)/√6

 

Multiply by √6/√6:

 

√6(√6√3 - √3)/6

 

√6√3(√6 - 1)/6

 

√18(√6 - 1)/6

Answer 2

1.

     √a + √b . √a +√b    = a + b + 2√ab

      √a - √b    √a + √b       a - b

 

2.

    Do the same thing multiply both numerator and denominator by conjugate value of denominator.

 

 3. can't be simplified

 

  4 .  √3 ( √6 - 2 √3) = √18 - 6 = 3 √2 - 6

 

  5. easy do it yourself.

 

  Have to grasp the idea.