# I'm stuck trying to figure out 8 square of 2 and 13 square root 3 in radical form i know the decimal is 33.83036899 but don't now the radical form can someone please help?

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8 #sqrt2# +13 #sqrt3#

8

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The square roots

In fact the set of numbers of the form

For example,

Attempting to solve:

#3 = (a+bsqrt(2))^2 = (a^2+2b^2)+2ab sqrt(2)#

We find that we require

If

If

Having shown

#a+bsqrt(2)+csqrt(3)+dsqrt(6) = 0#

Then if at least one of

#sqrt(3) = -(a+bsqrt(2))/(c+dsqrt(2))#

#color(white)(sqrt(3)) = -((a+bsqrt(2))(c-dsqrt(2)))/(c^2-2d^2)#

#color(white)(sqrt(3)) = (ad-bc)/(c^2-2d^2)+(bc-ad)/(c^2-2d^2)sqrt(2)#

which contrdicts our earleir finding.

Therefore:

#a+bsqrt(2)+csqrt(3)+dsqrt(6) = 0" " => " "a=b=c=d=0#

Hence the representation

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