How do you simplify $(5 + sqrt 3) /( 2 - sqrt3)$ ?

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Answer 1 · 2016-04-11T14:21:35

$(5+sqrt(3))/(2-sqrt(3))=13+7sqrt(3)$

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

You can write the value 1 in many ways: $2/2; 16/16; or 1=(2+sqrt(3))/(2+sqrt(3))$

Multiply by 1 but in the form $1=(2+sqrt(3))/(2+sqrt(3))$ giving

$(5+sqrt(3))/(2-sqrt(3)) xx (2+sqrt(3))/(2+sqrt(3))" "=" "( (5+sqrt(3))(2+sqrt(3)))/(2^2 -[(sqrt(3))^2])$

$=> (10+5sqrt(3)+2sqrt(3)+3)/(4-3)$

$=>13+7sqrt(3)$

How do you simplify (5 + sqrt 3) /( 2 - sqrt3)(5 + sqrt 3) /( 2 - sqrt3)?