Question

Prove that √[(√3-√2)/(√3+√2)] = 0.318, where √3 = 1.732 and √2 = 1.414​

Answer 1

Explanation:

${\large{\underline{\underline{\bf{\purple{Question \: : - }}}}}}$

${\underline{\underline{\sf{\red{Prove \: That :-}}}}}$

$\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}} = 0.318}} \end{gathered}$

$\small{\underline{\underline{\sf{\red{Where :-}}}}}$

$\bf{\green{\sqrt{3}}}$ = 1.732

$\bf{\green{\sqrt{2}}}$ = 1.414

$\begin{gathered}\end{gathered}$

$\large{\underline{\underline{\bf{\purple{Solution \: : - }}}}}$

$\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}} = 0.318}} \end{gathered}$

$\begin{gathered}\end{gathered}$

$\red \divideontimes$ Here, we have provided that 3 = 1.732 and 2 = 1.414. So, we put the given values in equation.

$\begin{gathered}\end{gathered}$

$\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}} = 0.318}} \end{gathered}$

$\begin{gathered}\end{gathered}$

$\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{1.732 - 1.414}{{1.732 + 1.414}}} = 0.318}} \end{gathered}$

$\begin{gathered}\end{gathered}$

$\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{0.318}{3.146}} = 0.318}} \end{gathered}$

$\begin{gathered}\end{gathered}$

$\begin{gathered} \dashrightarrow{\sf{\sqrt{\cancel{\dfrac{0.318}{3.146}}} = 0.318}} \end{gathered}$

$\begin{gathered}\end{gathered}$

$\begin{gathered} \dashrightarrow{\sf{ \sqrt{0.101} = 0.318}} \end{gathered}$

$\begin{gathered}\end{gathered}$

$\begin{gathered} \dashrightarrow{\sf{0.318 = 0.318}} \end{gathered}$

$\begin{gathered}\end{gathered}$

$\begin{gathered} \dashrightarrow{\underline{\underline{\sf{ \red{LHS = RHS }}}}} \end{gathered}$

$\begin{gathered}\end{gathered}$

${\bigstar{\overline{\underline{\boxed{\textsf{\textbf{\green{Hence Proved !}}}}}}}}$