Question

rationalise the denominator 7/ root + root 3

Answer 1

Answer:

Step-by-step explanation:

\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 think it help u