# how to represente root 13 on a number line

Draw a number line (l) and mark the points O, A, B  and C such that OA = AB = BC = 1

Draw CD ⊥ l, such that CD = 1 units.

Join OC

In right ΔOCD,

OD2 = OC2 + CD2

Taking O as centre and D as radius, draw an arc which cuts l in F

Now, draw EF ⊥ l, such that EF = 1 units

Join OE'

In right ΔOEF,

OE2 = OF2 + EF2

Taking O as centre and OE as radius, draw an arc which cuts l in H

Now, draw GH ⊥ l, such that GH = 1 units

Join OG

In right ΔOGH,

Taking O as centre and OG as radius, draw an arc which cuts l in J.

Now, draw IJ ⊥ l, such that IJ = 1 units

Join OI,

In right ΔOIJ,

Taking O as centre and OI as radius, draw an arc which cuts l in L.

The point L represents on the number line.

• 13

to represent root 13on the number line u should first applypythagoras theorem to root 1,2,3,4,5,6,7,8,9,10,11,12 respictively and after constructing root 13 draw an arc with the radius of the perpindicular

• -1

Since 13 is not a square number there is no exact real answer, [ but you can find an approximate value using the following (Newton-Raphson) iteration formula: xn+1=xn - (x2n -13)/(2xn) Using this formula the square root of 13 can be stated as 3.605551275 to 10 s.f. after 3 iterations starting from 3.5. Further iterations would yield even more accurate solutions to more significant figures. Alternatively, just use a calculator. ]

• 6
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