Question

find square root of 318096 ;y long division

Answer 1

here is ur answer for the problem

Answer 2

Step-by-step explanation:

318,096 is clearly a multiple of 16 (96 = 6×16; 318 is even, thus a multiple of 2 and every multiple of 1,000 is a multiple of 8). As 16 = 2 × 2 × 2 × 2,

318,096 = 2 × 2 × 2 × 2 × 19,881

Adding the digits of 19,881, we have 1 + 9 + 8 + 8 + 1 = 27, which is a multiple of 9; this means that 19,881 is a multiple of 9 = 3 × 3

So 318,096 = 2 × 2 × 2 × 2 × 3 × 3 × 2,209

Now, 2,209 is not even nor a multiple of 3 or 5, so it looks like we will have to use trial and error to find the factors. I can clearly see that 7 and 11 aren’t factors, but now it’s getting a little tricky. I still have 13, 17, 19, and so on. How far do I have to go? Well, 50 squared = 2,500, which is greater than 2,209; thus, we need not consider any prime factors over 50 - in fact, we need go no further that 47. Hang on, what is 47 squared? Why, it is 2,209!

So 318,096 = 2 × 2 × 2 × 2 × 3 × 3 × 47 × 47 =24×32×472

The principal square root of 318,096 is thus 22×3×47(=564)