Question

Rationalise the denominator of 1/[7+3√3]​

Answer 1

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Answer 2

Answer:

After rationalization,the number is

$\frac{7 - 3 \sqrt{3} }{22}$

Step-by-step explanation:

The given irrational number is

$\frac{1}{7 + 3 \sqrt{3} }$

In order to rationaluse any irrational number,we shall follow the steps as shown below.Let the number be

$\frac{1}{a + b \sqrt{c} }$

After rationalisation,it becomes

$\frac{1}{a + b \sqrt{c} } \times \frac{a - b \sqrt{c} }{a - b \sqrt{c} } = \frac{a - b \sqrt{c} }{ {a}^{2} - {b}^{2} c}$

Repeating the same steps for the given number we get

$= > \frac{1}{7 + 3 \sqrt{3} } \times \frac{7 - 3 \sqrt{3} }{7 - 3 \sqrt{3} } \\ = \frac{7 - 3 \sqrt{3} }{ {7}^{2} - {(3 \sqrt{3}) }^{2} } = \frac{7 - 3 \sqrt{3} }{22}$

Hence after rationalisation the given number becomes

$\frac{7 - 3 \sqrt{3} }{22}$

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