Question

Simplyfy the rationalising the denominator 1/3root2-2root3​

Answer 1

Aŋsweʀ

Rationalising The Denominator :

$\sf \dashrightarrow \: \frac{1}{ 3\sqrt{2} - 2 \sqrt{3} } \\ \\ \sf \dashrightarrow \: \frac{1}{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \\ \\ \sf \dashrightarrow \:\frac{3 \sqrt{2} + 2 \sqrt{3} }{9 \times 2 - 4 \times 3} \\ \\ \sf \dashrightarrow \: \frac{3 \sqrt{2} + 2 \sqrt{3} }{18 - 12} \\ \\ \sf \dashrightarrow \: \frac{3 \sqrt{2} + 2 \sqrt{3} }{6}$

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Answer 2

Answer:

1/3√2-2√3.

Rationalising denominator of 3√2-2√3 is 3√2+2√3.

Multiply numerator & denominator by 3√2+2√3.

1/3√2-2√3×3√2+2√3/3√2+2√3.

3√2+2√3/(3√2)²-(2√3)². (Because (a-b)×(a+b)=a²-b² where a=3√2 & b=2√3).

3√2+2√3/(9×2)-(4×3).

3√2+2√3/18-12.

3√2+2√3/6.

I think this is your answer.