If \(\sqrt { x } \) is an irrational number, then x is:

1

(a)

rational

(b)

irrational

(c)

0

(d)

real

The simplified form of \(\frac { { 13 }^{ \frac { 1 }{ 5 } } }{ { 13 }^{ \frac { 1 }{ 3 } } } \) is

1

(a)

\({ 13 }^{ \frac { 2 }{ 15 } }\)

(b)

\({ 13 }^{ \frac { 8 }{ 15 } }\)

(c)

\({ 13 }^{ \frac { 1 }{ 3 } }\)

(d)

\({ 13 }^{ \frac { 2 }{ 15 } }\)

If \({ 8 }^{ x }=\frac { 64 }{ { 2 }^{ x } } \) , then the value of x is

1

(a)

3

(b)

1

(c)

1/2

(d)

3/2

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

1

(a)

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

Is the product of two irrational numbers always an irrational number?

1

(a)

No, it may be rational or irrational.

Find the value of \(\sqrt[3]{625^{-2}}\)

1

(a)

\(\sqrt[3]{625^{-2}}\) = (625^-2)^1/4 = (625^-2x1/4)
= (625^-1/2)
= \((\frac{1}{625})^{1/2}=\frac{1}{25}\)

Write the rationalizing factor of \(\frac{1}{\sqrt{50}}\) .

1

(a)

\(\frac{1}{\sqrt{50}}=\frac{1}{\sqrt{5\times5\times2}}\)
=\(\frac{1}{5\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}}{10}\)
So, rationalizing factor is \(\sqrt{2}\)

Find five rational numbers between 1 and 2.

2

(a)

Divide \(8\sqrt { 15 } \) by \(2\sqrt { 3 } \)

2

(a)

Classify the following numbers as rational or irrational: \(\frac { 2\sqrt { 7 } }{ 7\sqrt { 7 } } \)

3

(a)

If \(x={ \left( 2+\sqrt { 5 } \right) }^{ \frac { 1 }{ 2 } }+{ \left( 2-\sqrt { 5 } \right) }^{ \frac { 1 }{ 2 } }\) and \(y={ \left( 2+\sqrt { 5 } \right) }^{ \frac { 1 }{ 2 } }-{ \left( 2-\sqrt { 5 } \right) }^{ \frac { 1 }{ 2 } }\) , then evaluate \({ x }^{ 2 }+{ y }^{ 2 }\)

3

(a)

Find two irrational numbers between 0.1 and 0.12.

4

(a)

Find two irrational numbers between \(\frac { 1 }{ 7 } \) and \(\frac { 2 }{ 7 } \)

4

(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)