Q. 3

# We have seen in Class 7 that any odd number can be written as the difference of two perfect squares. (The lesson, Identities) Usingthis, draw lines of lengths centimetres.

Any odd number can be written in the form 2k – 1,k being a natural number.

Now,2k – 1 = k2 – (k – 1)2

● For,

2k – 1 = 7

2k = 8

k = 4

So, √7 = 42 – 32

So, if we draw a line of 4 units, say CD, then,

Then,

Draw a random line and cut a length of 3c.m. s off it, to have AB.

Then draw a normal BA’ on AB.

Draw a circular arc with A as the centre and CD as centre, which eventually intersects BA’ at E.

Join B and E; and, A and E.

See, In Δ ABE, –

AB BE

BE2 = AE2 – AB2 = 42 – 32 = 7

E = √7 c.m.

● And,

2k – 1 = 11

2k = 12

k = 6

So, √11 = √( 62 – 52)

Draw a random line and cut a length of 5 c.m. s off it, to have AB.

Then draw a normal BA’ on AB.

Draw a circular arc with A as the centre and CD as centre, which eventually intersects BA’ at E.

Join B and E; and,A and E.

See, In Δ ABE, –

AB BE

BE2 = AE2 – AB2 = 62 – 52 = 11

óBE = √11 c.m.

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