Question

verified answer required​

Answer 1

Answer:

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

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

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

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

• $\bf{\green{\sqrt{3}}}$ = 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

${\large{\underline{\underline{\bf{\purple{Learn \: More \: : - }}}}}}$

★ For any two real numbers a and b, a, b ≠ 0, and for any two positive integers, m and n.

$\red \divideontimes$ If a be any non - zero rational number, then

• ➠ a^0 = 1

$\red \divideontimes$ If a be any non - zero rational number and m,n be integer, then

• ➠ (a^m)^n = a^mn

$\red \divideontimes$ If a be any non - zero rational number and m be any positive integer, then

• ➠ a^-m = 1/a^m

$\red \divideontimes$ If a/b is a rational number and m is a positive integer, then

• ➠ (a/b)^m = a^m/b^m

$\red \divideontimes$ For any Integers m and n and any rational number a, a ≠ 0

• ➠ a^m × a^n = a^m+n

$\red \divideontimes$ For any Integers m and n for non - zero rational number a,

• ➠ a^m ÷ a^n = a^m-n

$\red \divideontimes$ If a and b are non - zero rational numbers and m is any integer, then

• ➠ (a+b)^m = a^m × b^m

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