Answer:
98
Step-by-step explanation:
To find the square root of 9604 using prime factorization we have to rewrite the number 9604 using a multiplication of prime factors.
Take the prime numbers in order from least towards greatest 2,3,5,7,11,13,...and check if they divide evenly with our number 9604.
→If the number ends in an even number is divisible by 2
is 9604 divisible by 2? yes so do
9604 /2 = 4802
is 4802 divisible by 2? yes so do
4802/2 = 2401
is 2401 divisible by 2? no so check the divisibility by 3 (second prime number)
→If the sum of all digits is a multiple of 3 the number is divisible by 3
is 2401 divisible by 3?
2+4+0+1 = 7 is not a multiple of 3 so no, so check divisibility by 5
→If the number ends in 0 or 5 is divisible by 5
is 2401 divisible by 5? no so check divisibility by 7
→If the difference of the number without the last digit and double of the last digit is a multiple of 7 then the number is divisible by 7
is 2401 divisible by 7
240- 2*1 = 240 -2 = 238
23-2*8 = 23-16 = 7 so yes the number 2401 is divisible by 7
2401/7 = 343
is 343 divisible by 7 yes because 34-2*3= 34-6 = 28 is a multiple of 7
343/7 =49
is 49 divisible by 7 yes
49/7 = 7
is 7 divisible by 7 yes
7/7 = 1
The number 9604 can be written as
9604 = 2*2* 7*7*7*7
The square root 9604 is
√9604 = √2*2*7*7*7*7 = 2*7*7 = 98
