Question

represent √2,√3and√5 on real line​

Answer 1

Solution

How to draw √2 ,√3 and √5 on the number line .

• Diagrams in Attachment !

Construction :-

• Step 1 : take 1 unit from 0 and draw a perpendicular at that point .

• Step 2: join line to the hypotenuse

• keep compass on the point zero and pencil point on top of triangle and draw an Arc .

• the point obtained is √x .

• now draw one unit perpendicular at √x and similarly draw hypotenuse.

√2 case :-

ABC is a right angle triangle .

AB ^2 = BC ^2 + AC ^2

=> AB^2 = 1^2 +1^2

=> AB^2 = √1^2+1^2

=>AB^2 = √2

√3 case :-

PBQ is also a right angle triangle where ,

PB^2 =PQ ^2 + BQ^2

=> PB^2 =√2^2 + 1^2

=>PB ^2 =√ 2+1

=> PB^2 = √3