to construct √x on number line and explain its method
Answers
Given : root x
√x
To find : How to draw / locate on number line
Solution:
Draw a number line .
Mark a point A on - x on number line ( x unit left of zero )
& mark a point B on 1 on number line
Draw perpendicular bisector of A & B which cuts number line at M
Draw a semi circle taking M as center & MA = MB radius
Draw a perpendicular at MO ( O being 0 )
which intersect drawn semicircle at C
Taking O as center & compass width = OC , draw an arc on right side of Zero
intersecting number line at P
P is √x on number Line
Verification
AB =x+ 1
Radius = MA = MB = MC = (x+ 1 )/ 2
OM = MB - OB =(x+ 1 )/ 2 - 1 = (x - 1)/2
OC² = MC² - MO²
=> OC² = ( (x+ 1 )/ 2)² - ( (x - 1)/2 )²
Using a² - b² = (a + b )(a - b)
=> OC² = (x) (1)
=> OC = √x
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