Mathematics

Problem

## EXERCISE 1.4 1. Classify the following numbers as rational or irrational: (i)

2-\sqrt{5}

(ii)

(3+\sqrt{23})-\sqrt{23}

(iii)

\frac{2 \sqrt{7}}{7 \sqrt{7}}

(iv)

\frac{1}{\sqrt{2}}

(v)

2 \pi

2. Simplify each of the following expressions: (i)

(3+\sqrt{3})(2+\sqrt{2})

(ii)

(3+\sqrt{3})(3-\sqrt{3})

(iii)

(\sqrt{5}+\sqrt{2})^{2}

(iv)

(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})

3. Recall,

\pi

is defined as the ratio of the circumference (say

c

) of a circle to its diameter (say

d

). That is,

\pi=\frac{c}{d}

. This seems to contradict the fact that

\pi

is irrational. How will you resolve this contradiction? 4. Represent

\sqrt{9.3}

on the number line. 5. Rationalise the denominators of the following: (i)

\frac{1}{\sqrt{7}}

(ii)

\frac{1}{\sqrt{7}-\sqrt{6}}

(iii)

\frac{1}{\sqrt{5}+\sqrt{2}}

(iv)

\frac{1}{\sqrt{7}-2}

(i)

2-\sqrt{5}

(ii)

(3+\sqrt{23})-\sqrt{23}

(iii)

\frac{2 \sqrt{7}}{7 \sqrt{7}}

(iv)

\frac{1}{\sqrt{2}}

(v)

2 \pi