Question

find the value of 1 / 1+√2​

Answer 1

AnswEr :

›»› The value is -1 + √2

Given :

• 1/1 + √2

To Find :

• Calculate the value.

Solution :

$\tt{:\implies \dfrac{1}{1 + \sqrt{2} } }$

Find the conjugate irrational number of denominator,

$\tt{:\implies \dfrac{1}{1 + \sqrt{2} } \times \dfrac{1 - \sqrt{2} }{1 - \sqrt{2} } }$

The denominator is multiplied by denominator, and the numerator is multiplied by numerator,

$\tt{:\implies \dfrac{1 \big( 1 - \sqrt{2} \big)}{\big(1 + \sqrt{2} \big) \big(1 - \sqrt{2} \big)}}$

Multiply each term in parentheses by 1,

$\tt{:\implies \dfrac{1 - \sqrt{2} }{\big(1 + \sqrt{2} \big) \big(1 - \sqrt{2} \big)}}$

Expand the expression by using (a - b)(a+ b) = a² - b²,

$\tt{:\implies \dfrac{1 - \sqrt{2} }{ {1}^{2} - {\big( \sqrt{2} \big) }^{2} }}$

Calculate power,

$\tt{:\implies \dfrac{1 - \sqrt{2} }{1 - {\big( \sqrt{2} \big) }^{2} }}$

$\tt{:\implies \dfrac{1 - \sqrt{2} }{1 - 2}}$

Subtract 2 from 1,

$\tt{:\implies \dfrac{1 - \sqrt{2} }{ - 1} }$

Move the minus sign to the front of the fraction,

$\tt{:\implies - \dfrac{1 - \sqrt{2} }{1} }$

If the denominator is 1, the denominator can be removed,

$\tt{:\implies - \big(1 - \sqrt{2} \big)}$

Change the symbol of each term in parentheses when there is a (-) symbol in front of parentheses,

$\frak{: \implies \underline{ \boxed{ \pink{ \frak{- 1 + \sqrt{2} }}}}}$

║Hence, the value is -1 + √2.║