How do you simplify #sqrt18/(sqrt8-3) #?

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Answer 1 · 2016-05-21T14:48:22

#-12-9sqrt(2)" "# Using 'primary root' only

#-12+-9sqrt(2)" "#All solutions.

Using #a^2-b^2=(a+b)(a-b)#

Multiply by 1 but in the form of #1=(sqrt(8)+3)/(sqrt(8)+3)#

#(sqrt(18)(sqrt(8)+3))/((sqrt(8)-3)(sqrt(8)+3))#

#(sqrt(18)(sqrt(8)+3))/(8-3^2)#

But #sqrt(8)=2sqrt(2)" and "sqrt(18)=3sqrt(2)#

#(3sqrt(2)(2sqrt(2)+3))/(8-3^2)#

#color(brown)("Note that from above,"-3^2" is different to "(-3)^2)#

#(12+9sqrt(2))/(-1)#

#-12-9sqrt(2)" "# Using 'primary root' only

#-12+-9sqrt(2)" "#All solutions.