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Rationalise the denomitor (2sqrt6-sqrt5)/(3sqrt5-2sqrt5)

Rationalise the denomitor\newline26−535−25 \frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{5}}

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Full solution

Q. Rationalise the denomitor\newline26−535−25 \frac{2 \sqrt{6}-\sqrt{5}}{3 \sqrt{5}-2 \sqrt{5}}
  1. Simplify Denominator: Simplify the denominator: 35−253\sqrt{5} - 2\sqrt{5} simplifies to 5\sqrt{5} (since 3−2=13 - 2 = 1).
  2. Substitute Denominator: Substitute the simplified denominator back into the expression: (26−5)/5(2\sqrt{6} - \sqrt{5}) / \sqrt{5}
  3. Rationalize Denominator: Rationalize the denominator by multiplying numerator and denominator by 5\sqrt{5}:(26−5)⋅55⋅5\frac{(2\sqrt{6} - \sqrt{5}) \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = 26⋅5−55\frac{2\sqrt{6}\cdot\sqrt{5} - 5}{5}
  4. Simplify Expression: Simplify the expression:\newline2305−55\frac{2\sqrt{30}}{5} - \frac{5}{5}\newline= 2530−1\frac{2}{5}\sqrt{30} - 1

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