Proving a Number Is Irrational, Quiz

Which statement is the key step in proving

\sqrt{7}

irrational?

A If

7

divides

a + b

, then

7

divides

a

B If

7

divides

a^2

, then

7

divides

a

C If

a^2

is odd, then

a

is even

D If

7

divides

a

, then

a

is prime

In a proof that

\sqrt{3}

is irrational, we assume

\displaystyle \sqrt{3} = \dfrac{a}{b}

with

a

,

b

having no common factor. Squaring gives which equation?

A

3a^2 = b^2

B

a^2 = 3b

C

a = 3b^2

D

a^2 = 3b^2

In that proof, what contradiction is finally reached?

A

b

is larger than

a

B

a

and

b

both have the factor

3

C

a

and

b

are both zero

D

\sqrt{3}

is a whole number

Why does the step \"

p

divides

a^2

, so

p

divides

a

\" need

p

to be prime?

A Composite numbers never divide squares

B Only primes can divide a square

C It fails for primes larger than

10

D It fails for composites:

9

divides

6^2

but not

6

Given that

\sqrt{5}

is irrational, which number is irrational?

A

(\sqrt{5})^2 - 1

B

\displaystyle \dfrac{2\sqrt{5}}{\sqrt{5}}

C

\sqrt{5} \times \sqrt{5}

D

4 + 3\sqrt{5}

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Proving a Number Is Irrational, Quiz

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