Question

(i)
$(7 + 3 \sqrt{5} ) \div (7 - 3 \sqrt{5)}$
​

Answer 1

$\small\bold{Value \: of \: rationalization \: of \: \bold{\frac{7+3 \sqrt{5}}{7-3 \sqrt{5}}} }$

$\bold{ is \: equal \: to \bold{\frac{(47+21 \sqrt{5 )}}{2}} }$

Solution:

$\small \bold{To \: start \: with, \: rationalization \: we \: need \: to \: multiply \: 7+3 \sqrt{5}}$

with both the numerator and denominator to

$\small\bold{remove \: the \: roots. \: Multiplying \: 7+3 \sqrt{5}7+3 }$

we get,

$\frac{7+3 \sqrt{5}}{7-3 \sqrt{5}} \times \frac{7+3 \sqrt{5}}{7+3 \sqrt{5}}$

$\small\bold{\frac{(7+3 \sqrt{5})^{2}}{(7)^{2}-(3 \sqrt{5})^{2}}=\frac{49+42 \sqrt{5}+45}{49-45}=\frac{94+42 \sqrt{5}}{4} }$

$\bold{(we \: get \: the \: values \: in \: (a+b)^{2}}$

$\small \bold{mode \: in \: the \: numerator \: and \left(a^{2}-b^{2}\right)}$

mode in the denominator. Therefore, the primary value after multiplication is

Taking 2 common in both numerator and

$\bold{denominator \: we \: get \: \frac{94+42 \sqrt{5}}{4} }</p><p></p><p>$

$\bold{\frac{2(47+21 \sqrt{5})}{2.2}=\frac{(47+21 \sqrt{5})}{2}}$