Real Numbers, Course Quiz

What is the prime factorisation of

945

?

A

3^2 \times 5 \times 21

B

3^3 \times 5 \times 7

C

3^3 \times 35

D

3^2 \times 5 \times 7

150 = 2 \times 3 \times 5^2

and

180 = 2^2 \times 3^2 \times 5

. What is their HCF?

A

900

B

60

C

15

D

30

Using the same numbers, what is

\mathrm{LCM}(150, 180)

?

A

900

B

1800

C

450

D

27000

Which statement about

\mathrm{HCF} \times \mathrm{LCM} =

product of the numbers is correct?

A It fails only when all three are prime

B It fails only for even numbers

C It holds for two numbers but can fail for three, e.g.

3

,

6

,

12

D The identity always holds for three numbers

Why can

15^n

never end in the digit

0

?

A It has no factor

2

B It is always odd and prime

C It has no factor

3

D It has no factor

5

Which number is irrational?

A

\sqrt{12}

B

\sqrt{3} \times \sqrt{27}

C

\displaystyle \dfrac{\sqrt{18}}{\sqrt{2}}

D

\sqrt{49}

To prove

\sqrt{11}

irrational by contradiction, what do we assume first?

A

11

divides

a

B

\displaystyle \sqrt{11} = \dfrac{a}{b}

with

a

,

b

integers having no common factor,

b \neq 0

C

\sqrt{11}

is a whole number

D

\sqrt{11} = a + b

for integers

a

,

b

\mathrm{HCF}(a, 96) = 12

and

\mathrm{LCM}(a, 96) = 480

. Find

a

.

A

60

B

120

C

40

D

5

Two lights blink every

45

s and

60

s. After how many seconds do they next blink together?

A

2700

B

15

C

90

D

180

Given

\sqrt{2}

is irrational, which of these is rational?

A

5 - \sqrt{2}

B

\displaystyle \dfrac{\sqrt{2}}{3}

C

(4 + \sqrt{2}) + (1 - \sqrt{2})

D

1 + 2\sqrt{2}

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