Question

Express this with rational denominator b²/√(a²+b²)+a​

Answer 1

$</p><p>\rm \bf {\pink{ SOLUTION:-}} \\ \\ \\</p><p></p><p>\tt \: \frac {b^2}{ \sqrt {a^2 + b^2} + a} \\ \\</p><p></p><p>\texttt {\red { Rationalizing the denominator}} \\ \\</p><p></p><p>\tt \therefore \: = \: \frac {b^2}{ \sqrt {a^2 + b^2} + a} \times ( \frac{ \sqrt {a^2 + b^2} - a}{ \sqrt {a^2 + b^2} - a} \\ \\</p><p></p><p>\tt \therefore \: = \: \frac {b^2( \sqrt{a^2 + b^2} - a)}{a^2 + b^2 - a^2} \\ \\</p><p></p><p>\tt \therefore \: = \: \frac {b^2 ( \sqrt {a^2+b^2} - a)}{b^2} \\ \\</p><p></p><p>\tt \therefore \: = \: \sqrt {a^2 + b^2} - a \: \: is \: Answer \\ \\ \\ </p><p></p><p>\texttt { \red { Explanation of steps:-}} \\ \\ \\ \\</p><p></p><p>\tt (1) \: Multiply \: the \: fraction \: by \: \downarrow \\</p><p></p><p>\tt ( \frac { \sqrt {a^2 + b^2} - a}{ \sqrt {a^2 + b^2} - a}) \\ \\</p><p></p><p>\tt (2) \: Simply \: the \: products \\ \\</p><p></p><p>\tt (3) \: Eliminate \: the \: opposites \\ \\</p><p></p><p>\tt (4) \: Reduce \: the \: fraction \\</p><p>\tt by \: cancelling \: b^2 \\</p><p></p><p>\tt in \: \: numerator \: \: and \: \: denominator$