Which of the following is a rational number?

1

(a)

\(1+\sqrt { 3 } \)

(b)

\(\pi \)

(c)

\(2\sqrt { 3 } \)

(d)

0

Every rational number is:

1

(a)

a natural number

(b)

an integer

(c)

a real number

(d)

a whole number

A rational number lying between -3 and 3 is:

1

(a)

0

(b)

-4.3

(c)

-3.4

(d)

1.101 1001 10001...

A rational number lying between \(\sqrt { 2 } \) and \(\sqrt { 3 } \) is:

1

(a)

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

(b)

\(\sqrt { 6 } \)

(c)

1.6

(d)

1.9

The rational number between -1/5 and -2/5 is

1

(a)

0

(b)

-1/4

(c)

-3/10

(d)

-7/25

Is \(\frac{\sqrt{98}}{\sqrt{2}}\) a rational number or not?

2

(a)

\(\frac{\sqrt{98}}{\sqrt{2}}\)=\(\frac{\sqrt{98}}{\sqrt{2}}\) = √49 = 7
So, it is a rational number.

Write the simplest form of a rational number \(\frac{177}{413}\)

2

(a)

\(\frac{177}{413}\)= \(\frac{59\times3}{59\times7}=\frac{3}{7}\)

Calculate the decimal which represents the fraction \(\frac{7}{8}\)

2

(a)

\(\frac{7}{8}\)=0.875

Write a real number which has terminating decimal expansion.

2

(a)

\(\frac{31}{125}=0.248\)

Insert three rational numbers between \(\frac{-1}{3}\) and \(\frac{-2}{3}\)

2

(a)

\(\frac{-1}{3}\)=\(-\frac{4}{12}\)
and \(-\frac{2}{3}=-\frac{8}{12}\)
So three rational numbers are \(-\frac{5}{12},-\frac{6}{12}\)  and -\(\frac{7}{12}\)

Find two rational numbers between 0.1 and 0.2.

2

(a)

Find two rational numbers between 3/4 and 5/9.

2

(a)

Give three rational numbers between -3 and -2.

2

(a)

Find three rational numbers between -5/6 and 3/8.

2

(a)

Write three rational numbers between -2/5 and -1/5.

2

(a)

Is zero a rational number?can you write it in the form \(\frac { p }{ q } \),where p and q are integers and \(q\neq 0\)?

3

(a)

Find six rational numbers between 3 and 4.

3

(a)

Find five rational numbers between \(\frac { 3 }{ 5 } \) and \(\frac { 4 }{ 5 } \) 

3

(a)

Find four rational numbers between \(\frac { 3 }{ 7 } \)and \(\frac { 5 }{ 7 } \)

3

(a)

Find four rational numbers between \(\frac { 1 }{ 3 } \)and \(\frac { 4 }{ 5 } \)

3

(a)

Prove that: \({ \left( \frac { { x }^{ { a }^{ 2 } } }{ { x }^{ { b }^{ 2 } } } \right) }^{ \frac { 1 }{ a+b } }.{ \left( \frac { { x }^{ { b }^{ 2 } } }{ { x }^{ { c }^{ 2 } } } \right) }^{ \frac { 1 }{ b+c } }.{ \left( \frac { { x }^{ { c }^{ 2 } } }{ { x }^{ { a }^{ 2 } } } \right) }^{ \frac { 1 }{ c+a } }=1\)

5

(a)

If x = 3-2√2, find the value of √x+\(\frac{1}{\sqrt{x}}\)

5

(a)