Question

Use prime factorisation to work out the square root 9604.

Answer 1

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