Answered

Get the information you need from a community of experts on IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

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

Sagot :

SalmonWorldTopperidn

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]

Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Find reliable answers at IDNLearn.com. Thanks for stopping by, and come back for more trustworthy solutions.