Answer:
1.787
Step-by-step explanation:
[tex] \\ \sf \frac{5 + \sqrt{2} }{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } [/tex]
[tex] \\ \sf = \frac{(5 + \sqrt{2}) }{5 - \sqrt{2} } \times \frac{(5 + \sqrt{2}) }{5 + \sqrt{2} }[/tex]
[tex] \\ \sf = \frac{25 + 5 \sqrt{2 } + 5 \sqrt{2} + 2 }{( {5})^{2} - ( \sqrt{ {2}})^{2} } [/tex]
[tex] \\ \sf = \frac{27 + 10 \sqrt{2} }{25 - 2} [/tex]
[tex] \\ \sf = \frac{27 - 10 \sqrt{2} }{23} [/tex]
Now putting the value of√2
[tex] \\ \sf = \frac{27 + 10 \times 1.414}{23} [/tex]
[tex] \\ \sf = \frac{27 + 14.14}{23} [/tex]
[tex] \\ \sf = \frac{41.14}{23} [/tex]
[tex] \\ \sf = 1.787[/tex]
