How do you simplify 5 / [(sqr rt 6) + (sqr rt 11)] ?

Question

How do you simplify this problem, without a calculator: 5 / ({sqr rt 6} + {sqr rt 11}) ?

The final outcome should have no radicals in the denominator. I don't see any factors or anything that might be helpful...

Answer 1

5 / (√6 + √11)

= 5(√6 - √11) / (√6 + √11)(√6 - √11)

= 5(√6 - √11) / (6 - 11)

= 5(√6 - √11) / -5

= -(√6 - √11)

= √11 - √6

Answer 2

5 / [6^1/2 + 11^1/2]



(btw: ^ <-- this sign means to the power of)

Answer 3

5 / [(sqr rt 6) + (sqr rt 11)]

= 5 / [(sqr rt 6) + (sqr rt 11)] x1

5 / [(sqr rt 6) + (sqr rt 11)] x [(sqr rt 6) - (sqr rt 11)/[(sqr rt 6) - (sqr rt 11)

= 5([(sqr rt 6) - (sqr rt 11)/ (6-11)

= 5([(sqr rt 6) - (sqr rt 11)/ -5

= -([(sqr rt 6) - (sqr rt 11)}

= -(sqr rt 6) + (sqr rt 11)

= sqrt11-sqrt6

Answer 4

multiply denominator and numerator by sqrt6 - sqrt11 (use a^2 - b^2 = (a-b)a+b))

=[5*(sqrt6 - sqrt11)] / (5-11)

= - (sqrt6 - sqrt11)

= sqrt11 - sqrt6