Math help

My question is this: 

2 times the square root of 5

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

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

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)