#1**0 **

My question is this:

2 times the square root of 5

over------------------------------------------------------------------

2times the square root of 7 + 3 times the square root 3

Guest Apr 2, 2017

#2**+1 **

You should clarify your denominator. Is it 2sqrt(7) + 3sqrt(3)? Or, is it 2 sqrt(7+3) x sqrt(3)??

Guest Apr 2, 2017

#3**+1 **

2 sqrt (5) / [ 2 sqrt (7) + 3 sqrt (3) ]

Note that 2 sqrt (7) = sqrt (28) and 3 sqrt (3) = sqrt (27)

So we have

2 sqrt(5) / [ sqrt (28) + sqrt (27) ]

Multiply top/bottom by the conjugate of the denominator → [sqrt (28) - sqrt (27) ]]

And we have

[2 srqt (5)] [ sqrt (28) - sqrt (27)] / [ 28 - 27 ] =

[2 srqt (5)] [ sqrt (28) - sqrt (27)] / 1 =

[2 srqt (5)] [ sqrt (28) - sqrt (27)] =

[2 sqrt (5)] [ 2 sqrt (7) - 3 sqrt (3) ]=

4 sqrt (35) - 6 sqrt (15)

CPhill
Apr 2, 2017