Question

if√2= 1.4142 then find the value of 1+√2/3-2√2

Answer 1

Hi...☺

Here is your answer...✌

GIVEN THAT,

√2 = 1.4142 -----(1)

We have

$\frac{1 + \sqrt{2} }{ 3 - 2 \sqrt{2} } = \frac{1 + \sqrt{2} }{3 - 2 \sqrt{2} } \times \frac{3 + 2\sqrt{2} }{3 + 2\sqrt{2} } \\ \\ = \frac{(1 + \sqrt{2})(3 + 2\sqrt{2} ) }{ {3}^{2} - {(2 \sqrt{2}) }^{2} } \\ \\ = \frac{3 +2 \sqrt{2} + 3 \sqrt{2} + 4 }{9 - 8} \\ \\ = \frac{7 + 5 \sqrt{2} }{1} \\ \\ = 7+ 5 \times (1.4142) \: \: \: \: \: \: \: \: \: \: |from \: (1)|\\ \\ = 7 + 7.071 \\ \\ = 14.071$