Question

represent under root 3 in number line​

Answer 1

Answer:

square root of 3

Step-by-step explanation:

Again by pythogaras we get OC=3root. then by compass taking radius = OC ,draw an arc so that it cuts the number line at D then the distance at OD will be the square root of 3

Answer 2

$\large{\underline{\underline{\red{\sf{Given:}}}}}$

• $\tt{A\: Irrational\: number\:\sqrt{3}.}$

$\large{\underline{\underline{\red{\sf{To\:Do:}}}}}$

• $\tt{To\: represent\:\sqrt{3}\:on\: number\:line.}$

$\large{\underline{\underline{\red{\sf{Answer:}}}}}$

We will be using Pythagoras Theorem to represent √3 on the number line. For this we would have to first construct √2 , thereafter we will construct √3 using a pair of compasses.

$\underline{\purple{\bf{\leadsto Steps\:of\: construction:}}}$

$\tt{\orange{Step\:1:}\:\:\green{At\:O\: construct\:90^{\circ}.}}$

$\tt{\orange{Step\:2:}\:\:\green{Taking\:1u\:cut\:an\:arc\:on\:\perp.}}$

$\tt{\orange{Step\:3:}\:\:\green{Join\:C\:to\:A.}}$

$\tt{\orange{Step\:4:}\:\:\green{At\:C\: construct\:90^{\circ}.}}$

$\tt{\orange{Step\:5:}\:\:\green{Taking\:1u\:cut\:arc\:on\:\perp\:from\:C.}}$

$\tt{\orange{Step\:6:}\:\:\green{Join\:B\:to\:C.}}$

$\tt{\orange{Step\:7:}\:\:\green{Taking\:AB\:as\:radius\:and\:O\:as\: center\:cut\:arc\:on\: number\:line.}}$

$\underline{\pink{\tt{Hence\:AB\:=\sqrt{3}}}}$

____________________________________

$\underline{\purple{\bf{\leadsto Proof\:of\: construction:}}}$

$\green{\rm{\mapsto In\:\triangle\:OAC:}}$

$\tt{:\implies OC^2+OA^2=AC^2 }$

$\tt{:\implies 1^2+1^2=AC^2 }$

$\tt{:\implies AC^2=1+1}$

$\tt{:\implies AC^2=2}$

$\underline{\boxed{\red{\bf{\dag AC=\sqrt{2}}}}}$

____________________________________

$\green{\rm{\mapsto In\:\triangle\:ABC:}}$

$\tt{:\implies BC^2+AC^2=AB^2 }$

$\tt{:\implies (\sqrt{2})^2+1^2=AB^2 }$

$\tt{:\implies 2+1=AB^2 }$

$\tt{:\implies AB^2=3}$

$\underline{\boxed{\red{\bf{\dag AB=\sqrt{3}}}}}$

$\underline{\orange{\tt{Hence\:Proved.}}}$