How do you rationalize the denominator and simplify $2/(sqrt3+sqrt2)$ ?

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Answer 1 · 2017-01-15T04:38:16

$(2)/(sqrt3+sqrt2)=2(sqrt3-sqrt2)$

Simplify $(2)/(sqrt3+sqrt2)$

Rationalize the denominator using the difference of squares, $a^2-b^2=(a+b)(a-b)$ , where $a=sqrt3$ and $b=sqrt2$ .

$(2)/((sqrt3+sqrt2))*((sqrt3-sqrt2))/((sqrt3-sqrt2))=$

$(2(sqrt3-sqrt2))/((sqrt3+sqrt2)(sqrt3-sqrt2))=$

$(2(sqrt3-sqrt2))/(sqrt3^2-sqrt2^2)=$

Apply the rule $sqrt(a)^2=a$

$(2(sqrt3-sqrt2))/(3-2)=$

$(2(sqrt3-sqrt2))/1=$

$2(sqrt3-sqrt2)$

How do you rationalize the denominator and simplify 2/(sqrt3+sqrt2)2/(sqrt3+sqrt2)?