Question

Rationalise 1/5+root2​

Answer 1

Answer:

(5 - √2) / 23

Step-by-step explanation:

1 / (5 + √2)

= 1 x (5 - √2) / (5 + √2) x (5 - √2)

(a + b)(a - b) = a² - b². Here a = 5 and b= √2

= (5 - √2) / (5² - (√2)²)

= (5 - √2) / (25 - 2)

= (5 - √2) / 23

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Answer 2

$\large{explanation}$

$\frac{1}{5 + \sqrt{2} }$

$\frac{1}{5 + \sqrt{2} } \times \frac{5 - \sqrt{2} }{5 - \sqrt{2} }$

$\frac{5 - \sqrt{2} }{(5) { } ^{2} - ( \sqrt{2)} {}^{2} }$

$\frac{5 - \sqrt{2} }{25 - 2}$

$\frac{5 - \sqrt{2} }{23}$