Quiz about Number System

Question 1

Classify the number:

Accepted Answer

rational, real

Answer

integer, rational, real

Answer

irrational, real

Answer

whole, integer, rational, real

Question 2

Which of the following is irrational?

Accepted Answer

$$\sqrt{7}$$

Answer

$$\sqrt{\frac{4}{9}}$$

Answer

$$\sqrt{\frac{12}{3}}$$

Answer

$$\sqrt{81}$$

Question 3

$$2\sqrt{3}+\sqrt{3}$$ is equal to

Accepted Answer

$$3\sqrt{3}$$

Answer

$$2\sqrt{6}$$

Answer

6

Answer

$$4\sqrt{6}$$

Question 4

The number obtained on rationalising the denominator of $$\frac{1}{\sqrt{7}-2}$$ is

Accepted Answer

$$\frac{\sqrt{7}+2}{3}$$

Answer

$$\frac{\sqrt{7}-2}{3}$$

Answer

$$\frac{\sqrt{7}+2}{5}$$

Answer

$$\frac{\sqrt{7}+2}{45}$$

Question 5

After rationalising the denominator of

$$\frac{7}{3\sqrt{3}-2\sqrt{2}}$$ , we get the denominator as

Accepted Answer

19

Answer

13

Answer

5

Answer

35

Question 6

the number is ( $$3-\sqrt{3}$$ )( $$3-\sqrt{3}$$ )

Accepted Answer

an irrational number

Answer

a rational number

Answer

not a natural number

Answer

none of these

Question 7

$$A\ rational\ number\ between\ \frac{1}{7}\ and\ \frac{2}{7}\ is$$

Accepted Answer

$$\frac{5}{21}$$

Answer

$$\frac{1}{14}$$

Answer

$$\frac{2}{21}$$

Answer

$$\frac{5}{14}$$

Question 8

$$2-\sqrt{7}is\ $$

Accepted Answer

an irrational number

Answer

a rational number

Answer

an integer

Answer

a natural number

Question 9

$$On\ simplifying\ \left(\sqrt{5\ }+\sqrt{7}\right)²,\ we\ get$$

Accepted Answer

$$12+2\sqrt{35}$$

Answer

12

Answer

$$\sqrt{35}$$

Answer

$$\sqrt{5}+\sqrt{7}$$

Question 10

Simplify $$\sqrt{125}\ imes\sqrt{5}$$

Accepted Answer

25

Answer

5

Answer

35

Answer

50

Question 11

$$Multiply\ 6\sqrt{5}by\ 2\sqrt{5}$$

Accepted Answer

60

Answer

70

Answer

80

Answer

50

Question 12

$$Add\ 2\sqrt{2}+\ 5\sqrt{3}\ \ and\ \sqrt{2}-3\sqrt{3}$$

Accepted Answer

$$3\sqrt{2}\ +2\sqrt{3}$$

Answer

$$\sqrt{2\ \ }-\sqrt{3}$$

Answer

$$3\sqrt{2}-2\sqrt{3}$$

Answer

$$\sqrt{3}+\sqrt{2}$$

Question 13

What is the definition of integers?

Accepted Answer

Whole numbers and their opposites

Answer

Numbers you count on your fingers and toes

Answer

Natural numbers and zero

Answer

Terminating or repeating decimals

Question 14

$$If\ x=3+2\sqrt{2}\ ,then\ \ the\ value\ \ find\ x+\frac{1}{x}$$

Accepted Answer

6

Answer

5

Answer

7

Answer

8

Question 15

$$Find\ the\ value\ of\ a\ and\ b\ if\ \frac{\sqrt{3}\ -1}{\sqrt{3}\ +1}=a+b\sqrt{3}$$

Accepted Answer

a=2,b=-1

Answer

a=1,b=2

Answer

a=3,b=1

Answer

a=-1,b=2

Question 16

$$simplify\ \frac{4+\sqrt{5}}{4-\sqrt{5}}\ +\ \frac{4-\sqrt{5}}{4+\sqrt{5}}$$

Accepted Answer

42/11

Answer

22/3

Answer

32/11

Answer

52/11

Question 17

$$If\ x=\frac{\sqrt{2\ }\ +1}{\sqrt{2}\ -1}\ and\ y=\frac{\sqrt{2}-1}{\sqrt{2}+1},\ find\ the\ value\ of\ x^2+y^2+xy$$

Accepted Answer

35

Answer

45

Answer

25

Answer

55

Question 18

$$Find\ the\ value\ of\ \left(81\right)^{0.16}\ X\ \left(81\right)^{0.09}$$

Accepted Answer

3

Answer

1

Answer

6

Answer

2

Question 19

$$Evaluate\ \left(\frac{32}{243}\right)^{\frac{-4}{5}}$$

Accepted Answer

81/16

Answer

27/16

Answer

8/27

Answer

27/8

Question 20

$$simplify\ \ \ 64^{\frac{-1}{3}}\left\{64^{\frac{1}{3}}-64^{\frac{2}{3}}\right\}$$

Accepted Answer

-3

Answer

3

Answer

1/3

Answer

-1/3

Question 21

$$if\ x=5\ and\ y=2,\ find\ the\ value\ of\ \ \left(x^y+y^x\right)$$

Accepted Answer

57

Answer

37

Answer

67

Answer

47

Question 22

$$Add\ 2\sqrt{2}+\ 5\sqrt{3}\ \ and\ \sqrt{2}-3\sqrt{3}$$

Accepted Answer

$$3\sqrt{2}\ +2\sqrt{3}$$

Answer

$$\sqrt{2\ \ }-\sqrt{3}$$

Answer

$$3\sqrt{2}-2\sqrt{3}$$

Answer

$$\sqrt{3}+\sqrt{2}$$

Question 23

$$\frac{p}{q}$$ form of $$0.\overline{6}$$ is

Accepted Answer

$$\frac{2}{3}$$

Answer

$$\frac{2}{33}$$

Answer

$$\frac{1}{3}$$

Answer

$$\frac{11}{13}$$

Question 24

For positive real numbers a and b, which is not true?

Accepted Answer

$$\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)=a^2-b$$

Answer

$$\sqrt{ab}=\sqrt{a} imes\sqrt{b}$$

Answer

$$\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$$

Answer

$$\left(a+\sqrt{b}\right)\left(a-\sqrt{b}\right)=a^2-b$$

Question 25

if $$\frac{1}{7}=0.\overline{142857}$$ , then $$\frac{3}{7}$$ equals

Accepted Answer

$$0.\overline{428571}$$

Answer

$$0.\overline{571428}$$

Answer

$$0.\overline{857142}$$

Answer

$$0.\overline{285718}$$

Question 26

$$\left(\sqrt{3}+2\right)\left(\sqrt{2}+3\right)\ Equals\ to$$

Accepted Answer

$$\sqrt{6}+3\sqrt{3}+2\sqrt{2}+6$$

Answer

$$12+2\sqrt{2}+3\sqrt{3}$$

Answer

$$2\sqrt{3}+3\sqrt{2}+6+\sqrt{6}$$

Answer

$$\sqrt{6}+6$$

Question 27

Find which of the variables x, y, z and u represent irrational number :

Accepted Answer

$$x^2=5$$

Answer

$$y^2=9$$

Answer

$$z^2=.04$$

Answer

$$u^2=\frac{17}{4}$$

Question 28

every rational number is

Accepted Answer

a real number

Answer

a natural number

Answer

an integer

Answer

a whole number

Question 29

$$2^{\frac{1}{3}} imes\ 2^{\frac{1}{6}}$$ is equal to

Accepted Answer

$$2^{\frac{1}{2}}$$

Answer

2

Answer

$$2^{\frac{1}{3}}$$

Answer

3

Question 30

$$\left(3^{\frac{1}{2}}\right)^{\frac{1}{3}}$$ is equal to

Accepted Answer

$$3^{\frac{1}{6}}$$

Answer

$$3^{\frac{1}{2}}$$

Answer

$$3^{\frac{1}{3}}$$

Answer

$$3^{\frac{1}{5}}$$

Number System

32 questions

Classify the number:

Which of the following is irrational?

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