pratu043
How do you find the rationalising factor of root2 + root7  root10?



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pratu043
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dw:1344951900463:dw

mathslover
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multiply that by its conjugate @pratu043 what do you get?

pratu043
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By conjugate you mean:
dw:1344952032255:dw

mathslover
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\[\large{(\sqrt{2}+\sqrt{7}\sqrt{10})(\sqrt{2}+\sqrt{7}+\sqrt{10})=?}\]

mathslover
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dw:1344952080072:dw

mathslover
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@pratu043 what do you get by multiplying that.. ?

pratu043
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How do you find the conjugate?

pratu043
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I only know how to find for binomial surds.

mathslover
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@pratu043 let the expression given be like this:
\[\large{(\sqrt{2}+\sqrt{7})(\sqrt{10})}\]

mathslover
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I meant to say that:
a+bc = (a+b)(c)
right?

pratu043
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yes

mathslover
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dw:1344952309566:dw

pratu043
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dw:1344952351465:dw
What do you do with  root10?

pratu043
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dw:1344952415376:dw
sorry

mathslover
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ok leave that for once...
what will be the conjugate of a+b ?

pratu043
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ab

mathslover
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right so let a = c+d and b = b
now can u tell me what will be the new conjugate? :
(c+d)+(b) conjugate = ?

pratu043
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(c+d)  (b)

mathslover
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right so what will be the conjugate of :
\[\large{(\sqrt{2}+\sqrt{7})(\sqrt{10})}\]

pratu043
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dw:1344952630671:dw
ok, I got the conjugate part.

mathslover
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right now :
multiply this conjugate with original expression

pratu043
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dw:1344952686106:dw
right?

mathslover
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good so we have:
\[\large{2\sqrt{14}1}\]
now:(√2 + √7  √10)[(√2 + √7 + √10) (2√14 + 1)]
do this

pratu043
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dw:1344952926110:dw

pratu043
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But why should we do this?

mathslover
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it is a step towards the answer

mathslover
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also try to check that out pratu that u did: can that be more simplified?

mathslover
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@pratu043 you there?

pratu043
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sorry yes i am there.

pratu043
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do you mean that we should try and convert the irrationals in that expression to mixed surds?

mathslover
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yes

pratu043
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I think I can handle it on my own now, thanks!!

mathslover
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(√2 + √7  √10)[(√2 + √7 + √10) (2√14 + 1)]
\[\large{(\sqrt{2}+\sqrt{7}\sqrt{10})(\sqrt{2}+\sqrt{7}+\sqrt{10})(2\sqrt{14}+1)}\]
\[\large{(9+2\sqrt{14}10)(2\sqrt{14}+1)=(2\sqrt{14}1)(2\sqrt{14}+1)=561=55}\]

mathslover
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nice to hear best of luck