Question

Rationalise the denominator
1+√2/2-√2

Answer 1

Hii friend,

1+✓2/2-✓2

=> 1+✓2/2-✓2 × 2+✓2/2+✓2

=> (1+✓2) (2+✓2)/ (2-✓2) (2+✓2)

=> 1(2+✓2) + ✓2(2+✓2) / (2)² - (✓2)²

=> 2+✓2 + 2✓2 + ✓2 × ✓2 / 4 - 2

=> 2+✓2+2✓2+2/2

=> 4+3✓2/2....Ans....

HOPE IT WILL HELP YOU...... :-)

Answer 2

Hey friend,
Here is the answer you were looking for:
$\frac{1 + \sqrt{2} }{2 - \sqrt{2} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{1 + \sqrt{2} }{2 - \sqrt{2} } \times \frac{2 + \sqrt{2} }{2 + \sqrt{2} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{1 \times 2 + 1 \times \sqrt{2} + \sqrt{2} \times 2 + \sqrt{2} \times \sqrt{2} }{ {(2)}^{2} - {( \sqrt{2} )}^{2} } \\ \\ = \frac{2 + \sqrt{2} + 2 \sqrt{2} + 2}{4 - 2} \\ \\ = \frac{4 + 3 \sqrt{2} }{2} \\ \\ (or \: we \: can \: write )\\ \\ = 2 + \frac{3 \sqrt{2} }{2}$


Hope this helps!!!

@Mahak24

Thanks...
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