Question

Calculate square root of the following numbers by Dvanda yoga method or Duplex process:

(a) 169744

(b) 10329796

Answer 1

(a) 169744

Steps:

(i) 16 – 4² = 0, New dividend = 09, Divisor = 4 x 2 = 8.

(ii) 9 ÷ 8, Quotient digit = 1, Remainder = 1.

(iii) New dividend = 17,

Adjusted dividend = 17 – 1² = 16.

(iv) 16 ÷ 8, Quotient digit = 2, Remainder = 0.

(v) Final remainder 

= 0.4 – 2 x 1 x 2

= 0

Therefore, square root of 169744 is 412.

(b) 10329796

Steps:

(i) 10 – 3² = 1, New dividend = 13, Divisor = 3 x 2 = 6.

(ii) 13 ÷ 6, Quotient digit = 2, Remainder = 1.

(iii) New dividend = 12,

Adjusted dividend = 12 – 2² = 8.

(iv) 8 ÷ 6, Quotient digit = 1, Remainder = 2.

(v) New dividend = 29,

Adjusted dividend = 29 – 2 x 1 x 2 = 25

(vi) 25 ÷ 6, Quotient digit = 4, Remainder = 1

(vii) New dividend = 17

Now find final remainder as follows:

(viii) 17 – (2 x 4 x 2 + 1²) = 0

(ix) 9 – 2 x 1 x 4 = 1

(x) 16 – 4² = 0