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

Number Systems

Exercise 1.4

Exemplar solutions class 9 chapter 1 exercise 4
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Class 9

Number Systems

Exercise 1.4

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

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

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

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 \(\frac{4}{(216)^{-\frac{2}{3}}}\)\(+\frac{1}{(256)^{-\frac{3}{4}}}\)\(+\frac{2}{(243)^{-\frac{1}{5}}}\).