Exemplar Solutions Class 9 Chapter 1 Number Systems Exercise 1 Question 1

1. Express (0.6+0.bar{7}+0.4bar{7}) in the form (frac{p}{q}), where p and q are integers and (qne {0}).

Number Systems

Exercise 1.4

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Class 9

Number Systems

Exercise 1.4

1. Express (0.6+0.bar{7}+0.4bar{7}) in the form (frac{p}{q}), where p and q are integers and (qne {0}).

2. Simplify: (frac{7sqrt{3}}{sqrt{10}+sqrt{3}})(-frac{2sqrt{5}}{sqrt{6}+sqrt{5}})(-frac{3sqrt{2}}{sqrt{15}+3sqrt{2}}).

3. If (sqrt{2}=1.414, sqrt{3}=1.732), then find the value of  (frac{4}{3sqrt{3}-2sqrt{2}})(+frac{3}{3sqrt{3}+2sqrt{2}}).

4. If (a=frac{3+sqrt{5}}{2}), then find the value of (a^2+frac{1}{a^2}).

5. If (x=frac{sqrt{3}+sqrt{2}}{sqrt{3}-sqrt{2}}) and (y=frac{sqrt{3}-sqrt{2}}{sqrt{3}+sqrt{2}}), then find the value of (x^2+y^2).

6. Simplify: ((256)^{-(4^{-frac{3}{2}})}).

7. Find the value of (frac{4}{(216)^{-frac{2}{3}}})(+frac{1}{(256)^{-frac{3}{4}}})(+frac{2}{(243)^{-frac{1}{5}}}).

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