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

Sagot :

SalmonWorldTopper

Explanation:

[tex]{\large{\underline{\underline{\bf{\purple{Question \: : - }}}}}}[/tex]

[tex]{\underline{\underline{\sf{\red{Prove \: That :-}}}}}[/tex]

[tex] \begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}} = 0.318}} \end{gathered}[/tex]

[tex]\small{\underline{\underline{\sf{\red{Where :-}}}}}[/tex]

[tex]\bf{\green{\sqrt{3}}}[/tex] = 1.732

[tex]\bf{\green{\sqrt{2}}}[/tex] = 1.414

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\large{\underline{\underline{\bf{\purple{Solution \: : - }}}}}[/tex]

[tex]\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}} = 0.318}} \end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

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

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{\sqrt{3} - \sqrt{2}}{\sqrt{3} + \sqrt{2}}} = 0.318}} \end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{1.732 - 1.414}{{1.732 + 1.414}}} = 0.318}} \end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow{\sf{\sqrt{\dfrac{0.318}{3.146}} = 0.318}} \end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow{\sf{\sqrt{\cancel{\dfrac{0.318}{3.146}}} = 0.318}} \end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow{\sf{ \sqrt{0.101} = 0.318}} \end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow{\sf{0.318 = 0.318}} \end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]\begin{gathered} \dashrightarrow{\underline{\underline{\sf{ \red{LHS = RHS }}}}} \end{gathered}[/tex]

[tex]\begin{gathered}\end{gathered}[/tex]

[tex]{\bigstar{\overline{\underline{\boxed{\textsf{\textbf{\green{Hence Proved !}}}}}}}}[/tex]

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