Question

If root 2=1.4142,find root2/ 2+root2

Answer 1

$\huge{\underline{\underline{Question\::-}}}$

If the value of $\sqrt{2}$ = 1.4142 then find the value of $\dfrac{\sqrt{2}}{ 2 + \sqrt{2}}$

$\huge{\underline{\underline{Answer\::-}}}$

$\underline{\underline{Given\::-}}$

$\sqrt{2}$ = 1.4142

$\underline{\underline{Solution\::-}}$

♦ To solve

• First we have to rationalize the denominator

• We have to simplify the obtained results

♦ Rationalizing

$\dfrac{\sqrt{2}}{ 2 + \sqrt{2}}$

=$\dfrac{\sqrt{2}}{ 2 + \sqrt{2}} \times \dfrac{ 2 - \sqrt{2}}{ 2 - \sqrt{2}}$

= $\dfrac{\sqrt{2}( 2 - \sqrt{2})}{ (2)^2 - (\sqrt{2)^2}}$

= $\dfrac{2 \sqrt{2} - ( \sqrt{2})^2 }{ 4 - 2 }$

= $\dfrac{2 \sqrt{2} - 2 }{ 2 }$

= $\dfrac{ 2 (\sqrt{2} - 1) }{ 2 }$

= $\sqrt{2} - 1$

♦ Now substituting the value of $\sqrt{2}$ = 1.4142

= $\sqrt{2} - 1$

= 1.4142 - 1

= 0.4142