Rationalize 3 by 2 root 3 - 3 root 2
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3/(2√3 - 3√2)
= 3(2√3 + 3√2)/(2√3 - 3√2)(2√3 + 3√2)
{multiplying both numerator and denominator by (2√3 + 3√2) }
= 3(2√3 + 3√2)/[ (2√3)^2 - (3√2)^2 ]
{ (a-b)(a+b) = a^2 - b^2 }
= 3(2√3 + 3√2)/[12 - 18]
= 3(2√3 + 3√2)/(-6)
= (2√3 + 3√2)/(-2)
= -(2√3 + 3√2)/2
= - √3 + 3√2/2
=
3√2 - √3
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2
= 3(2√3 + 3√2)/(2√3 - 3√2)(2√3 + 3√2)
{multiplying both numerator and denominator by (2√3 + 3√2) }
= 3(2√3 + 3√2)/[ (2√3)^2 - (3√2)^2 ]
{ (a-b)(a+b) = a^2 - b^2 }
= 3(2√3 + 3√2)/[12 - 18]
= 3(2√3 + 3√2)/(-6)
= (2√3 + 3√2)/(-2)
= -(2√3 + 3√2)/2
= - √3 + 3√2/2
=
3√2 - √3
-----
2
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