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.

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