Question

The number √2 is shown on a number line. Steps are given to Show √3 on the number line using √2 . fill in the boxes properly and complete the activity

Answer 1

Given :  The number √2 is shown on a number line.

To Find :  Show √3 on the number line using √2

Solution:

Let say O is the 0 on number line and  A represent √2

Draw a perpendicular at A on  OA

Take a length of 1 unit from A  on angle drawn and mark  as B

Using compass with = OB and taking O as center cut the line number line at C

Point  C represents √3 on the number line

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Answer 2

Answer:

see image

Step-by-step explanation:

• The point Q on the number line shows the number √2.

• A line perpendicular to the number line is drawn through the point Q. Point R is at unit distance from Q on the line.

Right angled A ORQ is obtained by drawing seg OR.

I(OQ) = √2, 1(QR) = 1

by pythagoras theorem,

$\rm [I(OR)]^{2} = [(OQ)]²+ [1(QR)]²$

$\rm= ( \sqrt{2} ) ^{2} +1²$

$=2+1$

$= 3$

$\therefore \rm \: I(OR) = \sqrt{3}$

Draw an arc with centre O and radius OR. Mark the point of intersection of the line and the arc as C. The point C shows the number line √3.