Question

Prove that 1/3+√7+1/√7+√5+1/√5+√3+1/√3+1=1

Answer 1

I think answer is 38

Answer 2

Step-by-step explanation:

$\bf \frac{1}{3 + \sqrt{7} } + \frac{1}{ \sqrt{7} + \sqrt{5} } + \frac{1}{ \sqrt{5} + \sqrt{3} } + \frac{1}{ \sqrt{3} + 1} = 1 \\ \\ \tt \large \: RATIONALISING \: \: THE \: \: ABOVE \\ \\ \bf \frac{3 - \sqrt{7} }{9 - 7 } + \frac{ \sqrt{7} - \sqrt{5} }{ 7 - 5 } + \frac{ \sqrt{5} - \sqrt{3} }{5 - 3 } + \frac{ \sqrt{3} - 1}{ 3 - 1} = 1 \\ \\ \bf \frac{3 - \cancel{\sqrt{7} + \sqrt{7} - \sqrt{5} + \sqrt{5} - \sqrt{3} + \sqrt{3} }- 1}{ 2} = 1 \\ \\ \huge \bf \fcolorbox{red}{grey}{1 = 1}$