Question

what is the value of denominator after rationalization 7/√5√3​

Answer 1

${\fbox{\huge{\tt{Solution\::}}}}$

7/√5√3 × √5√3/√5√3

7√5√3/15

Answer 2

Answer:

Heya !!!

Using the identities :

{(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ (x + y)(x - y) = {x}^{2} - {y}^{2}

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

On rationalizing the denominator we get,

= \frac{7 + 3 \sqrt{5} }{7 - 3 \sqrt{5} } \times \frac{7 + 3 \sqrt{5} }{7 + 3 \sqrt{5} } \\ \\ = \frac{ {(7)}^{2} + {(3 \sqrt{5} )}^{2} + 2(7)(3 \sqrt{5} )}{ {(7)}^{2} - {(3 \sqrt{5}) }^{2} } \\ \\ = \frac{49 + 45 + 42 \sqrt{5} }{49 - 45} \\ \\ = \frac{94 + 42 \sqrt{5} }{4} \\ \\ = \frac{47 + 21 \sqrt{5} }{2} \\