Question

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

Answer 1

=root{ [ root2  + 1] /[ root2 - 1 ]
=root{ [ root2  + 1] [root2 + 1] /[ root2 - 1 ][ root2 +1]}
=root{[root2 + 1]^2 / (root2)^2  - 1^2}
=root { [root 2 +1]^2 / 2-1}
=root{[root2 +1]^2}
=root2 +1
=1.414+1
=2.414//

Answer 2

Answer: 2.4142

Step-by-step explanation:

• We need to first rationalise the denominator and then put the value of $\sqrt{2}$ in the result obtained.
• $\sqrt{\frac{\sqrt{2}+1 }{\sqrt{2}-1 } }$

    ⇒ $\sqrt{\frac{\sqrt{2}+1 }{\sqrt{2}-1 } *\frac{\sqrt{2}+1 }{\sqrt{2}+1 } }$

    ⇒ $\sqrt{\frac{(\sqrt{2}+1)^{2} }{1 }}$

    ⇒$\sqrt{2}+1$

    ⇒ 1.4142+1

    ⇒2.4142

• Hence,the result of the given expression  is 2.4142.

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