Question

rationalize the denominator 4 / root 7 + root 3

Answer 1

$\frac{4}{ \sqrt{7} + \sqrt{3} }$

By Rationalization,

$\frac{4}{ \sqrt{7} + \sqrt{3} } \times \frac{ \sqrt{7} - \sqrt{3} }{ \sqrt{7} - \sqrt{3} } \\ \\ \\ \\ \frac{4( \sqrt{7} - \sqrt{3} )}{( \sqrt{7} + \sqrt{3})( \sqrt{7} - \sqrt{3}) }$

On denominator, by identity, a² - b² = (a + b)(a - b)


$\frac{4( \sqrt{7} - \sqrt{3}) }{ {( \sqrt{7} })^{2} - {( \sqrt{3} })^{2} } \\ \\ \\ \frac{4( \sqrt{7} - \sqrt{3} )}{7 - 3} \\ \\ \\ \frac{4( \sqrt{7} - \sqrt{3} )}{4} \\ \\ \\ \sqrt{7} - \sqrt{3}$



I hope this will help you


(-:

Answer 2

Heya !!!



4/ ✓7 + ✓3



=> 4 / ✓7 + ✓3 × ( ✓7-✓3) / ( ✓7-✓3)





=> 4 ( ✓7 - ✓3) / ( ✓7 + ✓3) ( ✓7-✓3)




=> 4✓7 - 4✓3 / (✓7)² - (✓3)²



=> 4✓7 - 4✓3 / 7-3


=> 4✓7 - 4✓3 /4


=> 4( ✓7 - ✓3) /4


=> ✓7 - ✓3




★ HOPE IT WILL HELP YOU ★