Mathematics

Problem

Answer the following with reference to the point that represents

\sqrt{2}

on the number line. a. (i) State the meaning of the principle that every real number corresponds to exactly one point on a straight line and every point on that line corresponds to exactly one real number. b. (ii) Point

O

represents

0

and point

A

represents

1

on the number line. From

A

, a segment

AB

of length

1

unit is drawn perpendicular to the line. The end

B

is joined to

O

. Explain clearly why the point

P

where

OB

meets the number line corresponds to

\sqrt{2}

. c. (iii) Show that

\sqrt{2}

cannot be expressed in the form

\dfrac{p}{q}

where

p

and

q

are integers,

q\ne0

. d. (iv) Write

\sqrt{2}

correct to four decimal places.

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