SOLUTION: please help me to simlify: √252- 5√6+√294-3√(1/(6 ))

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Question 736877: please help me to simlify: √252- 5√6+√294-3√(1/(6 ))
Answer by Susan-math(40) About Me  (Show Source):
You can put this solution on YOUR website!
Factor 252 = 2(126)=(2)(2)(63)=(2)(2)(3)(21)=(2)(2)(3)(3)(7)
So sqrt%28252%29=%282%29%283%29sqrt%287%29=6sqrt%287%29
Factor 294=(2)(147)=(2)(3)(49)=(2)(3)(7)(7)
So sqrt%28294%29=7sqrt%286%29
Rationalize the denominator of sqrt%281%2F6%29by multiplying by sqrt%286%29%2Fsqrt%286%29 to get
sqrt%286%29%2F6. So 3%2Asqrt%281%2F6%29+=+3%2Asqrt%286%29%2F6+=sqrt%286%29%2F2
So now we have: 6sqrt%287%29-5sqrt%286%29+%2B7sqrt%286%29+-+sqrt%286%29%2F2
And we can add like term with the same square root by adding their coefficients.
So we add -5+%2B+7+-+1%2F2+=+2-1%2F2+=+3%2F2 to get a final answer of
6sqrt%287%29+%2B3%2F2%2Asqrt%286%29