Question

If √2 = 1.414 then the value of 5+√2 / 5-√2 is

Answer 1

Answer:

1.787

Step-by-step explanation:

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

$\\ \sf = \frac{(5 + \sqrt{2}) }{5 - \sqrt{2} } \times \frac{(5 + \sqrt{2}) }{5 + \sqrt{2} }$

$\\ \sf = \frac{25 + 5 \sqrt{2 } + 5 \sqrt{2} + 2 }{( {5})^{2} - ( \sqrt{ {2}})^{2} }$

$\\ \sf = \frac{27 + 10 \sqrt{2} }{25 - 2}$

$\\ \sf = \frac{27 - 10 \sqrt{2} }{23}$

Now putting the value of√2

$\\ \sf = \frac{27 + 10 \times 1.414}{23}$

$\\ \sf = \frac{27 + 14.14}{23}$

$\\ \sf = \frac{41.14}{23}$

$\\ \sf = 1.787$