Question

if ✓3 = 1.732then the value of root under 2-✓3 by 2+✓3 ​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{\frac{2 - \sqrt{ 3} }{2 + \sqrt{ 3} } = 0.072}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given:}} \\ \tt: \implies \sqrt{3} = 1.732 \\ \\ \red{\underline \bold{To \: Find:}} \\ \tt: \implies \frac{2 - \sqrt{3} }{2 + \sqrt{3} } =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \\ \\ \tt \circ \:Multiplying \: \frac{ 2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \tt: \implies \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \tt: \implies \frac{(2 - \sqrt{3} )(2 - \sqrt{3}) }{(2 + \sqrt{3} )(2 - \sqrt{3} )} \\ \\ \tt \circ \: {a}^{2} - {b}^{2} = (a +b)(a -b) \\ \tt: \implies \frac{ (2 - \sqrt{3})^{2} }{ {2}^{2} - {( \sqrt{3} })^{2} } \\ \\ \tt: \implies \frac{(2 - \sqrt{3})^{2} }{4 - 3} \\ \\ \tt \circ \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \tt: \implies {2}^{2} + { (\sqrt{ 3} )}^{2} - 2 \times 2 \times \sqrt{3} \\ \\ \tt: \implies 4 + 3 - 4 \sqrt{3} \\ \\ \tt: \implies 7 - 4 \times 1.732 \\ \\ \tt: \implies 7 - 6.928 \\ \\ \green{\tt: \implies 0.072} \\ \\ \green{\tt \therefore \frac{2 - \sqrt{ 3} }{2 + \sqrt{ 3} } = 0.072}$

Answer 2

$\huge\purple{\underline{\underline{\pink{Ans}\red{wer:-}}}}$

$\sf{The \ value \ of \ \frac{2-\sqrt3}{2+\sqrt3} \ is \ 0.072}$

$\sf\orange{Given:}$

$\sf{\implies{\sqrt3=1.732}}$

$\sf\pink{To \ find:}$

$\sf{The \ value \ of \ \frac{2-\sqrt3}{2+\sqrt3}}$

$\sf\green{\underline{\underline{Solution:}}}$

$\sf{\implies{\frac{2-\sqrt3}{2+\sqrt3}}}$

$\sf{Rationalising \ the \ denominator}$

$\sf{\implies{\frac{(2-\sqrt3)(2-\sqrt3)}{(2+\sqrt3)(2-\sqrt3)}}}$

$\sf{By \ identity}$

$\sf{a^{2}-b^{2}=(a+b)(a-b)}$

$\sf{\implies{\frac{(2-\sqrt3)^{2}}{2^{2}-\sqrt3^{2}}}}$

$\sf{\implies{\frac{(2-\sqrt3)^{2}}{4-3}}}$

$\sf{\implies{\frac{(2-\sqrt3)^{2}}{1}}}$

$\sf{\implies{(2-\sqrt3)^{2}}}$

$\sf{By \ identity}$

$\sf{(a-b)^{2}=a^{2}-2ab+b^{2}}$

$\sf{\implies{(2-\sqrt3)^{2}=2^{2}-2(2)(\sqrt3)+\sqrt3^{2}}}$

$\sf{\implies{=4-4\sqrt3+3}}$

$\sf{\implies{=7-4(1.732}}$

$\sf{\implies{=7- 6.928}}$

$\sf{\implies{=0.072}}$

$\sf\purple{\tt{\therefore{The \ value \ of \ \frac{2-\sqrt3}{2+\sqrt3} \ is \ 0.072}}}$