Represent root 4.1 on number line.Write the justification.
Answers
Given : root 4 .1 √4.1
To find : represent on number line
Solution:
Step 1 : Draw a number line AOB ( O being 0)
Step 2 : Take a length of 4.1 cm from O on left side mark it M
Step 3 : Take 1 cm from O on right side , mark it N
Step 4 : Using suitable compass width draw arcs on both sides of MN taking M & N as center & intersecting at X & Y
Step 5 : join X & Y intersecting MN at P
Step 6 : Draw a semicircle taking P as center & PM = PN as radius ( compass width)
Step 7 : Draw a right angle at AO such that it intersect semicircle at Z
OZ = √4.1
Step 8 : Taking compass width = OZ and taking O as center cut the number line on right side at C
point C represent √4.1 on a number line
Mathematical proof
Semicircle radius = (4.1 + 1)/2 = 5.1/2 ( hypotenuse)
5.1/2 - 1 = 3.1/2 = Base
Perpendicular OZ² =( 5.1/2)² - (3.1/2)²
=> OZ² = (5.1/2 + 3.1/2) (5.1/2 - 3.1/2)
=> OZ² = 4.1
=> OZ = √4.1
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