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Answer» HEY friend,
Here is the answer you were looking for:

(i) \: \: \sqrt{( {5}^{2} - {4}^{2} )} \\ \\ = \sqrt{(25 - 16)} \\ \\ = \sqrt{(9)} \\ \\ = \sqrt{ {3}^{2} } \\ \\ we \: know \: that \\ \sqrt{ {a}^{2} } = a \\ \\ = 3


\sqrt{( {5}^{2} + {12}^{2}) } \\ \\ = \sqrt{(25 + 144)} \\ \\ = \sqrt{(169)} \\ \\ = \sqrt{ {13}^{2} } \\ \\ = 13


{( \frac{1}{2} )}^{2} + \sqrt{0.25} \\ \\ = \frac{1}{4} + \sqrt{ \frac{25}{100} } \\ \\ = \frac{1}{4} + \sqrt{ \frac{ {5}^{2} }{ {10}^{2} } } \\ \\ = \frac{1}{4} + \frac{5}{10} \\ \\ = \frac{1}{4} + \frac{1}{2} \\ \\ = \frac{1 \times 1 + 1 \times 2}{4} \\ \\ = \frac{1 + 2}{4} \\ \\ = \frac{3}{4}


( - \sqrt{ \frac{4}{9} } )( - \sqrt{ \frac{81}{100} } ) \\ \\ = ( - \sqrt{ \frac{ {2}^{2} }{ {3}^{2} } } )( - \sqrt{ \frac{ {9}^{2} }{ {10}^{2} } } ) \\ \\ = ( - \frac{2}{3} )( - \frac{9}{10} ) \\ \\ = - \frac{2}{3} \times - \frac{9}{10} \\ \\ = \frac{ - 2 \times - 9}{3 \times 10} \\ \\ = \frac{18}{30} \\ \\ = \frac{3}{5}

Hope this HELPS!!

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@Mahak24

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