Math, asked by rajeevkumarmzr, 5 months ago

18. Rationalize the denominators

4/√ 7+√ 3


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Answers

Answered by IIMidnightHunterII
1

Answer:

 =  \frac{4}{ \sqrt{7 }  +  \sqrt{3} }  \\  \\  =  \frac{4}{ \sqrt{7}  +  \sqrt{3} }  \times  \frac{ \sqrt{7} -  \sqrt{3}  }{ \sqrt{7}  -  \sqrt{3} }  \\  \\   \\ the \:  \:  \: denominator \:  \:  \: is \:  \:  \:  \: in \:  \:  \:  \: the \:  \:  \:  \: form \:  \:  \:  \\  \\ (x + y)(x - y) =  {x}^{2}  -  {y}^{2}  \\  \\ here \:  \:  \:  \: x =  \sqrt{7}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  y =  \sqrt{3}  \\  \\   = \frac{4 \times ( \sqrt{7} -  \sqrt{3} ) }{( \sqrt{7} +  \sqrt{3})( \sqrt{7}   -  \sqrt{3} ) }  \\  \\  =  \frac{4 \sqrt{7}  - 4 \sqrt{3} }{ { \sqrt{7} }^{2}  -  { \sqrt{3} }^{2} }  \\  \\  =  \frac{4 \sqrt{7}  - 4 \sqrt{3} }{7 - 3}  \\  \\  =  \frac{4 \sqrt{7}  - 4 \sqrt{3} }{4}

Answered by Manharankaur
0

Answer:

√7-√3

Step-by-step explanation:

=4/√7+√3 × √7-√3)√7-√3

=4(√7-√3)/(√7)^2-(√3)^2 [(a-b)(a+b)=a^2+b^2]

=4(√7-√3)/7-3

=4(√7-√3)/4

=√7-√3

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