Question

rationalise this question fastt

Answer 1

$\frac{ {b}^{2} }{ \sqrt{ {a}^{2} + {b}^{2} } +a }$


By Rationalization,


$\frac{ {b}^{2} }{( \sqrt{ {a}^{2} + {b}^{2}) + a } } \times \frac{ \sqrt{ {a}^{2} + {b}^{2} } - a }{ \sqrt{ {a}^{2} + {b}^{2} } - a} \\ \\ \\ \\ \\ \\ => \frac{ {b}^{2} ( \sqrt{ {a}^{2} + {b}^{2} } - a) }{( \sqrt{ {a ^{2} + {b}^{2} }})^{2} - {a}^{2} } \\ \\ \\ \\ \\ \\ => \frac{ {b}^{2} ( \sqrt{ {a}^{2} + {b}^{2} } - a)}{ {a}^{2} + {b}^{2} - {a}^{2} } \\ \\ \\ \\ \\ => \frac{ {b}^{2}( \sqrt{ {a}^{2} + {b}^{2} } - a) }{ {b}^{2} } \\ \\ \\ \\ => \sqrt{ {a}^{2} + {b}^{2} } - a$