Question

18. Rationalize the denominators

4/√ 7+√ 3


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Answer 1

Answer:

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

Answer 2

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