Question

locate root 3 on number line​

Answer 1

⦁First construct the BD of unit length perpendicular to OB.

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⦁Then apply the Pythagoras theorem $\rm{OD = \sqrt{(\sqrt{2})^{2} + 1^{2} = \sqrt{3}}}$

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⦁We can locate $\rm{\sqrt{3}}$ on number line by using a compass.

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⦁We know that, O is the center and radius OD. Now let's draw an arc which intersects the number line at the point Q.

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⦁Therefore, now the point Q = $\rm{\sqrt{3}}$

Answer 2

$\huge{\underline{\sf{Question :-}}}}$

1. Locate $\sqrt{3}$ on the number line.

$\huge{\underline{\sf{Answer :-}}}}$

✏ We can locate $\sqrt{3}$on the number line by using the Pythagoras theorem.

$\green{\underline\bold{We \:know,}}$

$\red{\underline\bold{By\:the\:pythagoras\:theorem,}}$

$\boxed{ \sf \purple{ (Hypotenuse)2\: = \: (Base)2 \:+\: (Height)2 }}$

⇒Hypotenuse =$\sqrt{(Base)2+(Height)2}$

⇒Hypotenuse =$\sqrt {(1)2+\sqrt{(2)2}}$

⇒Hypotenuse = $\sqrt {1+2}$

⇒Hypotenuse = $\sqrt{3}$

• ✏ For finding $\sqrt{3}$on the number line, first of all we have to locate$\sqrt{2}$on the number line.
• ✏ After locating $\sqrt{2}$on the number line, we can locate$\sqrt{3}$on the number line .

( Refer the given attachments for diagram.)

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