1.check whether root-16/root448 is a rational number or irrational number.

Question

2.if root3=1.732 then find value of square root 3-1/root3+1

Answer 1

since √448 = 8√7, which is clearly irrational, then
-16/8√7 = -2/√7 is clearly irrational

You probably meant (√3-1)/(√3+1) , but in the outcome it would not make any difference as to irrational vs rational

(√3-1)/(√3+1)
= (√3-1)/(√3+1) * (√3-1)/(√3-1)
= (3 - 2√3 + 1)/(3-1)
= 2 - √3, which is still irrational

using your approximate value of √ = appr 1.732
(√3-1)/(√3+1) = appr 2 - 1.732
= appr .268