Question

rational and irrational numbers class 9 icse.

Answer 1

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Here is the answer you were looking for:
$(1) \\ \frac{1}{ \sqrt{3} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{1}{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{1 \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } \\ \\ = \frac{ \sqrt{3} }{3} \\ \\ = \frac{1.732}{3} \\ \\ = 0.577 \\ \\ (2) \\ \frac{ \sqrt{2} + 1}{ \sqrt{5} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{ \sqrt{2} + 1 }{ \sqrt{5} } \times \frac{ \sqrt{5} }{ \sqrt{5} } \\ \\ = \frac{ \sqrt{2} \times \sqrt{5} + 1 \times \sqrt{5} }{ \sqrt{5} \times \sqrt{5} } \\ \\ = \frac{ \sqrt{10} + \sqrt{5} }{5} \\ \\ = \frac{3.162 + 2.236}{5} \\ \\ = \frac{5.398}{5} \\ \\ = 1.07 \\ \\ (3) \\ \frac{2 - \sqrt{3} }{ \sqrt{3} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ = \frac{2 - \sqrt{3} }{ \sqrt{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } \\ \\ = \frac{2 \times \sqrt{3} - \sqrt{3} \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } \\ \\ = \frac{2 \sqrt{3} - 3 }{3} \\ \\ = \frac{2 \times 1.732 - 3}{3} \\ \\ = \frac{3.464 - 3}{3} \\ \\ = \frac{0.464}{3} \\ \\ = 0.154$


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