Answered

Discover a world of knowledge and community-driven answers at IDNLearn.com today. Join our community to receive prompt and reliable responses to your questions from knowledgeable professionals.

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 using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Discover insightful answers at IDNLearn.com. We appreciate your visit and look forward to assisting you again.