Question

What are the steps to locate √5 on the number line.

Answer 1

Steps to locate $\sqrt{5}$ on a number line :

$\large{\boxed{\tt{ Spiral \:method}}}$

• Draw a number line .
• Take point O and A on it ; such that (OA) is 1 unit.
• Draw a line AB that would be perpendicular to (OA) making AB as 1 unit.
• Join line OB
• From ∆OAB we will find the value or measurement of line OB through the Pythagoras theorem which states : $\tt\green{ {Hypotenuse}^{2} = {Base}^{2} + {Perpendicular}^{2}}$

Following the same we will find out the value of OB

$\tt\green{ {(OB)}^{2} \implies {(OA)}^{2} + {(AC)}^{2}}$

$\tt\green{ {(OB)}^{2} \implies {1}^{2} + {1}^{2}}$

$\tt\green{ {(OB)}^{2} \implies 2}$

$\tt\green{ OB \implies \sqrt{2}}$

• Now draw a line BC perpendicular to OB such that BC is 1 unit.
• Now , join OC
• From ∆OBC using Pythagoras theorem we will find the value of OC

$\tt\green{ {(OC)}^{2} \implies {(OB)}^{2} + {(BC)}^{2}}$

$\tt\green{ {(OC)}^{2} \implies {\sqrt{2}}^{2} + {1}^{2}}$

$\tt\green{ {(OC)}^{2} \implies 2 + 1 }$

$\tt\green{ OC = \sqrt{3}}$

• Draw a perpendicular CD to OC such that CD is 1 unit.
• Join OD
• From ∆OCD = $\tt\green{ {(OD)}^{2} \implies {OC}^{2} + {DC}^{2}}$

$\tt\green{ {(OD)}^{2} \implies {\sqrt{3}}^{2} + {1}^{2}}$

$\tt\green{ {(OD)}^{2} \implies 3 + 1}$

$\tt\green { {OD}^{2} \implies 4}$

$\tt\green{ OD \implies \sqrt{4}}$

• Draw DE perpendicular to OD such that DE is 1 unit.
• Join DE
• From ∆ODE = $\tt\green{ {(OE)}^{2} \implies {OD}^{2} + {EO}^{2}}$

$\tt\green{ {(OE)}^{2} \implies {\sqrt{4}}^{2} + {1}^{2}}$

$\tt\green{ {(OE)}^{2} \implies 4 + 1}$

$\tt\green{ {OE}^{2} \implies 5}$

$\tt\green{ OE = \sqrt{5}}$

• Take O as the center and OE as the radius
• Draw an arc which cuts the number line at Point F.
• This point F is √5.