Represent -2 on the number line-

Draw a line AB ⊥ to number line, such that the length of AB is ⊥ unit. Join OB. Now, applying pythagoras theoram, OB^2 = OA^2 + AB^2 = 1 + 1 = 2 ⇒ OB = √(2) Ta ...

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Standard IX

Mathematics

Representation of Irrational Numbers on the Number Line

Represent √2 ...

Question

Represent $\sqrt{2}$ on the number line.

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Solution

Draw a line $A B ⊥$ to number line, such that the length of AB is $1$ unit.
Join OB. Now, applying pythagoras theoram,
$O B^{2} = O A^{2} + A B^{2} = 1 + 1 = 2$
$\Rightarrow O B = \sqrt{2}$
Take compass & taking O as centre & OB as radius, cut the number line. The distance OS will represent $\sqrt{2}$ units.

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Represent √2 on the number line.

Draw a line AB ⊥ to number line, such that the length of AB is 1 unit. Join OB. Now, applying pythagoras theoram, OB2=OA2+AB2=1+1=2 ⇒OB=√2 Take compass & taking O as centre & OB as radius, cut the number line. The distance OS will represent √2 units.

Represent $\sqrt{2}$ on the number line.