Question

2. Rationalise:
$\frac{1}{ \sqrt{7 } + \sqrt{3} - \sqrt{2} }$


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Answer 1

Answer:

Example 1:

{\displaystyle {\frac {10}{\sqrt {a}}}}{\frac {10}{\sqrt {a}}}

To rationalise this kind of expression, bring in the factor {\displaystyle {\sqrt {a}}}{\sqrt {a}}:

{\displaystyle {\frac {10}{\sqrt {a}}}={\frac {10}{\sqrt {a}}}\cdot {\frac {\sqrt {a}}{\sqrt {a}}}={\frac {10{\sqrt {a}}}{\left({\sqrt {a}}\right)^{2}}}}{\displaystyle {\frac {10}{\sqrt {a}}}={\frac {10}{\sqrt {a}}}\cdot {\frac {\sqrt {a}}{\sqrt {a}}}={\frac {10{\sqrt {a}}}{\left({\sqrt {a}}\right)^{2}}}}

The square root disappears from the denominator, because it is squared:

{\displaystyle {\frac {10{\sqrt {a}}}{\left({\sqrt {a}}\right)^{2}}}={\frac {10{\sqrt {a}}}{a}}}{\displaystyle {\frac {10{\sqrt {a}}}{\left({\sqrt {a}}\right)^{2}}}={\frac {10{\sqrt {a}}}{a}}}

This gives the result, after simplification:

{\displaystyle {\frac {10{\sqrt {a}}}{a}}}{\frac {10{\sqrt {a}}}{a}}

you can solve like this

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