What is the square root of 72? How to find the square root of 72?

The square root of 72 is 8.485. When we multiply the number by itself we get the square root of the number or the square number. It depends on the number for which the square root needs to be found. 
When the number 2 is squared 2² = 4
When 6 is squared 6² = 36
The √ 4 = 2.
The √ 36 = 6.

Before jumping straight into finding the square root of any number we must find whether the given number is a perfect square number or not. The numbers that end with 2,3,7 and 8 are considered perfect square numbers, and the numbers that end with 1,4,5,6, and 9 are not perfect square numbers.

The number 72 is not a perfect square number. Hence, it is tough to find the square root of 72. The square root of 72 can be found using the long division method. The square root is denoted using the symbol √ also called radix or radical symbol.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

Prime Factorization Method

• Step 1: Find the prime factors of 72.
  Prime factors of 72 = 2✕2✕2✕3✕3 
• Step 2: Group the similar numbers
  72 = 2√2 ✕3 
• Step 3: Take Square on both sides
  72 = 6√2
  Hence, the square root of 72 cannot be found using the prime factorization method. 

Long division method

Long division is one of the easiest methods to find the square root of any number. It was the preferred method to be used for the non-perfect square numbers. Find the integer that can divide the number and proceed with the long division. 

Steps to find the square root of 72:

• Step 1: Find the smallest integer that can divide the number. 
• Step 2: Keep following the long division using divisor and dividend. 
• Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.  

Find the square root of 72

• Step 1: Find the smallest integer that can divide the number. 72 is not a perfect root number and 8 is the nearest number that can divide it. 
• Step 2: Keep following the long division using divisor and dividend. 

Long division for 72

• Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.
• Hence, the √72 = 8.485

Solved Examples

Example 1: What is the square root of 72 using the long division method?
Solution:

√ 72 = 8.485
Example 2: What are the factors of 72?
Solution: The factors of 72 are 2,2,3 and 3. Though the number 72 has prime factors. The square root of the number cannot be found using the method.
Example 3: What is the square root of 64 using the prime factorization method?
Solution: 64 = 2 x 2 × 2 x 2 x 2 x 2 
Hence, the square of 64 is
√64 = 8
Example 4: What is the square root of 2 using the long division method?
Solution:

√2 = 1.4142
Example 5: Can you help Tom find the square root of 72 using the long division method?
Solution:

1. 72 – 1 = 71
2. 71 – 3 = 68
3. 68 – 5 = 63
4. 63 – 7 = 56
5. 56 – 9 = 47
6. 47 – 11 = 36
7. 36 – 13 = 23
8. 23 – 15 = 8
9. 8 – 17 = -9

The square root of 72 cannot be found using the repeated subtraction method.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

FAQs on the square root of 72