construct √5,√7,√2 on a number line
please diagram and matter pettandi
Answers
Answer:
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Step-by-step explanation:
Step I: Draw a number line and mark the center point as zero.
Step II: Mark right side of the zero as (1) and the left side as (-1).
Step III: We won’t be considering (-1) for our purpose.
Step IV: With 2 units as length draw a line from (1) such that it is perpendicular to the line.
Step V: Now join the point (0) and the end of new line of 2 units length.
Step VI: A right angled triangle is constructed.
Step VII: Now let us name the triangle as ABC such that AB is the height (perpendicular), BC is the base of triangle and AC is the hypotenuse of the right angled triangle ABC.
Step VIII: Now length of hypotenuse, i.e., AC can be found by applying Pythagoras theorem to the triangle ABC.
AC^2 = AB^2 + BC^2
⟹ AC^2 = 2^2 + 1^2
⟹ AC^2 = 4 + 1
⟹ AC^2 = 5
⟹ AC = √5
Step IX: Now with AC as radius and C as the centre cut an arc on the same number line and name the point as D.
Step X: Since AC is the radius of the arc and hence, CD will also be the radius of the arc whose length is √5.
Step XI: Hence, D is the representation of √5 on the number line.
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Let O be the origin on the line l.
Let A be on the line such that OA=1.
Draw AB perpendicular to OA at A such that AB=1. Then
OB^2 =OA^2+AB^2 = 1^2+1^2 = 2 Thus OB= root 2
With O as centre and OB as radius draw an arc cutting the line at C.
Then OC=OB= root 2
Again draw CD perpendicular to l such that CD=1. Then
OD^2=OC^2+CD^2 =2+1=3. Thus OD= root 3
Draw an arc with O as centre and OD as radius to cut l in E. Then OE=OD= root 3
Draw EF perpendicular to l at E such that EF = 2 and join OF. Now
OF^2=OE^2+EF^2=3+4=7
Hence OF = root 7
With O as centre and OF as radius, cut l at G.
Then OG=OF= root 7
Thus G represents root 7 on the line l.
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Step I: Draw a number line and mark the centre point as zero.
Step II: Mark right side of the zero as (1) and the left side as (-1).
Step III: We won’t be considering (-1) for our purpose.
Step IV: With same length as between 0 and 1, draw a line perpendicular to point (1), such that new line has a length of 1 unit.
Step V: Now join the point (0) and the end of new line of unity length.
Step VI: A right angled triangle is constructed.
Step VII: Now let us name the triangle as ABC such that AB is the height (perpendicular), BC is the base of triangle and AC is the hypotenuse of the right angled triangle ABC.
Step VIII: Now length of hypotenuse, i.e., AC can be found by applying pythagoras theorem to the triangle ABC.
AC^2= AB^2 + BC^2
⟹ AC^2 = 1^2 + 1^2
⟹ AC^2 = root 2
⟹ AC = √2
Step IX: Now with AC as radius and C as the centre cut an arc on the same number line and name the point as D.
Step X: Since AC is the radius of the arc and hence, CD will also be the radius of the arc whose length is √2.
Step XI: Hence, D is the representation of √2 on the number line.
