Question

5. Find the square root of 39204 by division method. ​

Answer 1

$390204 \\ </p><p>39204=4×19602 \\ </p><p>=4×9801 \\ </p><p>=4×99 ×99 \\ </p><p>= 2×2×9×11 ×11×9 \\ </p><p>=2×2×3×3×3×3×11×11 \\ </p><p>= 2^2× 3^4×11^2 \\ </p><p> = 2×3^2×11 =2×9×11=198 \\ </p><p>$

Answer 2

here is your answer:-

Number formed by tens and units is 04 . So, the number is divisible by 4.

Sum of digits is 18. So, the number is divisible by 9.

Sum of alternate digits is 9 for each of two sets. So, the number is divisible by 11.

Let us take 99 as factor (9 and 11).

39204=390×100+204

=390×99+390+204

=390×99+594

=390×99+600−6

=396×99

Now, we use divisibility by 4 .

396=99×4.

Hence,

39204=99×99×4

=(99×2)2.

Hence, required square root is

99×2

=198.

p.s.: Going strictly by Prime (power) factorization

30204=2234112

=(2×32×11)2.

So, the required seqareroot is

2×9×11

=198.

hope it will help you