Locate √8.7 on a number line.
Answers
Answer:
"take only example for to draw 8.7 do it yourself"
Mark the distance which is 8.4 from a point A on a given line to obtain a point B such that AB = 8.4 units. From B mark a distance of 1 unit and mark the new point as C . Find the mid point of AC and mark and that point as " O". Then Draw a semi circle with center O and radius OC .
Step-by-step explanation:
Step 1 : Draw a number line AOB ( O being 0)
Step 2 : Take a length of 8.7 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 = √8.7
Step 8 : Taking compass width = OZ and taking O as center cut the number line on right side at C
point C represent √8.7 on a number line
Mathematical proof
Semicircle radius = (8.7 + 1)/2 = 9.7/2 ( hypotenuse)
9.7/2 - 1 = 7.7/2 = Base
Perpendicular OZ² =( 9.7/2)² - (7.7)²
=> OZ² = (17.4)(2)/4
=> OZ² = 8.7
=> OZ = √8.7
