Question

correct answer will be marked as Brainliest
​

Answer 1

Step-by-step explanation:

2.15470054 is answer

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Answer 2

$\large\bf\underline\red{Answer \: :-}$

Given :

$\sf{ \frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1 } }$

Rationalization :

$\sf\longrightarrow{ \frac{ \sqrt{3} - 1 }{ \sqrt{3} + 1} \times \frac{ \sqrt{3} - 1}{ \sqrt{3} - 1 } }$

Here in numerator we use formula

(a-b)² = a² - 2ab + b²

In denominator we use formula

(a+b) (a-b) = a² - b²

$\sf\longrightarrow{ \frac{( \sqrt{3}) {}^{2} - 2( \sqrt{3})(1) + (1) {}^{2} }{( \sqrt{3}) {}^{2} - (1) {}^{2} } } \\ \\ \sf\longrightarrow{ \frac{3 - 2 \sqrt{3} + 1 }{3 - 1} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf\longrightarrow{ \frac{4 - 2 \sqrt{3} }{2} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

After rationalizing we get,

${\large{\leadsto{\underline{\boxed{\bf{\red{ \frac{4 - 2 \sqrt{3} }{2} }}}}}}}$

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Important Formula's

$\begin{gathered}\boxed{\begin{array}{c} \\ \tiny\bf{\dag}\:\underline{\frak{\rm{S}\frak{ome\:important\:algebric\:identities\:::}}} \\\\ \green{\bigstar}\:\rm \red{ (A+B)^{2} = A^{2} + 2AB + B^{2}} \\\\ \red{\bigstar}\rm\: \green{(A-B)^{2} = A^{2} - 2AB + B^{2}} \\\\ \orange{\bigstar}\rm\: \blue{A^{2} - B^{2} = (A+B)(A-B)}\\\\ \blue{\bigstar}\rm\: \orange{(A+B)^{2} = (A-B)^{2} + 4AB}\\\\ \pink{\bigstar}\rm\: \purple{(A-B)^{2} = (A+B)^{2} - 4AB}\\\\ \purple{\bigstar} \rm\: \pink{(A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}}\\\\ \gray{\bigstar}\rm\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\ \bigstar\rm\: \gray{A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})} \\\\ \end{array}}\end{gathered}$