To locate √on the number line,where n is a positive integer, we first locate
:a. n b. √− c. √+ d. √/
Answers
Given : locate root n on number line
To find : How to draw / locate
first locate
Solution:
-n is located first
Here is detailed process
Draw a number line .
Mark a point A on - n on number line
& 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 √n on number Line
Verification
AB = n + 1
Radius = MA = MB = MC = (n+1)/2
OM = MB - OB = (n+1)/2 - 1 = (n -1 )/2
OC² = MC² - MO²
=> OC² = ( (n+1)/2)² - ( (n-1)/2 )²
Using a² - b² = (a + b )(a - b)
=> OC² = (n) (1)
=> OC = √n
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