Question

square root of 1764 by prime factorization method

Answer 1

So, 1764 = 2² * 3² * 7²

and √(1764) = 2 * 3 * 7 = 42

Case b) Given number is not a perfect square

Let’s try N = 1771. We want x = √N.

1. Guess the nearest ‘round’ square, and take it as a first approximation of x.

40² = 1 600, so x = 40

2. Divide N by x : 1771/40 = 44,275

3. Take the average of 40 and 44,275 rounded to the nearest integer:

(40 + 44)/2 = 42, so now x = 42.

Answer 2

The square root of 1764 by prime factorization, we get

1764 = 2 x 2 x 3 x 3 x 7 x 7.  

√1764 = √(2 x 2 x 3 x 3 x 7 x 7)

= 2 x 3 x 7  

Therefore, √1764 = 42.