Question

find the square root by prime factorisation method 39204​

Answer 1

Dear Student,

★ Answer :

Square root by prime factorisation method 39204​ is 198

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★ Explanation :

Very good number for prime factorization.

⇒ 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.  

Note :  

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

30204 = 2²3⁴11²

⇒ So, the required Square root is  

2×9×11 = 198

Answer 2

Answer:

Using the steps above, here is the math showing you how to simplify square root of 39204.

39204 = 2233331111.

⇒ 39204 = 223232112

Therefore, √39204 = √(223232112)

⇒ √39204 = 23311 = 198.