Question

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

Answer 1

Step-by-step explanation:

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

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

`\begin{gathered} \dashrightarrow{\sf{\sqrt{(√(3) - √(2))/(√(3) + √(2))} = 0.318}} \end{gathered}`

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

`\bf{\green{√(3)}}` = 1.732

`\bf{\green{√(2)}}` = 1.414

`\begin{gathered}\end{gathered}`

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

`\begin{gathered} \dashrightarrow{\sf{\sqrt{(√(3) - √(2))/(√(3) + √(2))} = 0.318}} \end{gathered}`

`\begin{gathered}\end{gathered}`

`\red /ideontimes` 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{(√(3) - √(2))/(√(3) + √(2))} = 0.318}} \end{gathered}`

`\begin{gathered}\end{gathered}`

`\begin{gathered} \dashrightarrow{\sf{\sqrt{\frac{1.732 - 1.414}{{1.732 + 1.414}}} = 0.318}} \end{gathered}`

`\begin{gathered}\end{gathered}`

`\begin{gathered} \dashrightarrow{\sf{\sqrt{(0.318)/(3.146)} = 0.318}} \end{gathered}`

`\begin{gathered}\end{gathered}`

`\begin{gathered} \dashrightarrow{\sf{\sqrt{\cancel{(0.318)/(3.146)}} = 0.318}} \end{gathered}`

`\begin{gathered}\end{gathered}`

`\begin{gathered} \dashrightarrow{\sf{ √(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 !}}}}}}}}`