Question

rationalise the denominator​

Answer 1

Answer:

5-√21/4

Step-by-step explanation:

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Answer 2

$\huge{\fcolorbox{plum}{Lime}{Answer}}$

$\huge\mathbb\color{aqua} GIVEN:$

$⇒\frac{ \sqrt{7} \: - \sqrt{3} }{ \sqrt{7} + \sqrt{3} }$

$\huge\mathcal\color{Lime}FIND:$

$\mathcal\color{Lightpink}rationalize\: denominator$

$\huge\mathcal\orange{multipying\:with\:conjugate\:pair}$

$⇒ \frac{ \sqrt{7} - \: \sqrt{ 3} }{ \sqrt{7} + \sqrt{3} } \times \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} - \sqrt{3} }$

$\huge\mathcal\pink{★by\:using\:formulae★}$

★ (a + b) (a – b) = a² – b² ★

★ (a – b)² = a² – 2ab + b² ★

$⇒ \frac{( \sqrt{7} - \sqrt{3}) ^{2} }{ { (\sqrt{7}) }^{2} - ( \sqrt{3})^{2} }$

$⇒ \frac{( \sqrt{7})^{2} - \: 2( \sqrt{7} \times \sqrt{3} ) \: + ( \sqrt{3} )^{2} }{( \sqrt{7} )^{2} - ( \sqrt{3} )^{2} }$

$⇒ \frac{ 7 \: - \: 2\sqrt{21} \: + \: 3 }{7 \: - \: 3}$

$⇒ \frac{10 \: - 2 \sqrt{21} }{4} \: \:$

$⇒ \frac{2 \: (5 \: - \sqrt{21} )}{4}$

$⇒ \frac{\: 5 \: - \sqrt{21}}{2}$

$\huge\mathcal\color{plum}I\:hope\:it\:helps\:you.$