If a number has a non-terminating and non-recurring decimal expansion, then it is______________ .

(a)

a rational number

(b)

a natural number

(c)

an irrational number

(d)

an integer

Which of the following are irrational numbers?
\(\sqrt { 2+\sqrt { 3 } } \)
\(\sqrt [ 3 ]{ 5+\sqrt { 7 } } \)
\(\sqrt { 8-\sqrt [ 3 ]{ 8 } } \)
\(\sqrt { 4+\sqrt { 25 } } \)

(a)

(ii), (iii) and (iv)

(b)

(i), (ii) and (iv)

(c)

(i), (ii) and (iii)

(d)

(i), (iii) and (iv)

If \(\frac { 1 }{ 7 } \)= 0.142857, then the value of is______________.

(a)

0.285741

(b)

0.428571

(c)

0.285714

(d)

0.574128

The product of \(2\sqrt { 5 } \) and \(6\sqrt { 5 } \) is_______________.

(a)

\(12\sqrt { 5 } \)

(b)

60

(c)

40

(d)

\(8\sqrt { 5 } \)

The value of \(\bar { 0.03 } \) +\(\bar { 0.03 } \)  is ___________.

(a)

\(\bar { 0.09 } \)

(b)

\(\bar { 0.09 } \)

(c)

\(\bar { 0.09 } \)

(d)

0

In simple form,\(\sqrt [ 3 ]{ 54 } \) is ?

(a)

\(3\sqrt [ 3 ]{ 2 } \)

(b)

\(3\sqrt { 27 } \)

(c)

\(3\sqrt { 2 } \)

(d)

\(\sqrt { 3 } \)

\(\sqrt [ 4 ]{ 405 } =h\sqrt [ 4 ]{ 5 } \), then h = ____________

(a)

5

(b)

4

(c)

2

(d)

3

Rationalising the denominator \(\cfrac { 1 }{ \sqrt [ 3 ]{ 3 } } \)  ___________

(a)

3

(b)

\(\cfrac { { 3 }^{ \frac { 2 }{ 3 } } }{ 3 } \)

(c)

\(\sqrt { 3 } \)

(d)

\(\sqrt [ 3 ]{ 3 } \)

\(\cfrac { \sqrt [ 3 ]{ 27 } }{ \sqrt [ 5 ]{ 3 } } \) is equal to_______

(a)

\(5\sqrt { 9 } \)

(b)

\(5\sqrt { 6 } \)

(c)

\(5\sqrt { 24 } \)

(d)

\(\sqrt [ 5 ]{ 30 } \)

The length of a square is 1.2\(\times\)10³ m. Its area is_______

(a)

14.4 \(\times\) 10⁶

(b)

1.44 \(\times\) 10⁶

(c)

0.144 \(\times\) 10

(d)

1440