how to contruct sqrt 5,10, 29, 7 on the no. line

Question

how to contruct sqrt 5,10, 29, 7 on the no. line

Answer 1

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Construct a suitable right angled triangle on the number line. Note that

√5 = √(2^2 + 1^2)..........[Draw a right angled triangle with base = 2, height = 1]

√10 = √(3^2 + 1^2)........[Draw a right angled triangle with base = 3, height = 1]

√29 = √(5^2 + 2^2)........[Draw a right angled triangle with base = 5, height = 2]

For √7, it is more complicated:

√2 = √(1^2 + 1^2).......[Draw a right angled triangle with base = 5, height = 2]

√3 = √[(√2)^2 + 1^2]

..............[Draw a right angled triangle with base = √2, height = 1]

√7 = √((√3)^2 + 2^2)

..............[Draw a right angled triangle with base = √3, height = 2]

Hope that you know what I mean......