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Square Root

What Is the Square Root of 32? | How to Find the Square Root of 32?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 32? | How to Find the Square Root of 32?

What Is the Square Root of 32? | How to Find the Square Root of 32?

The square root of 32 is 5.656 mentioned with a symbol √. The square root of 32 is denoted using √32 or 321/2. The square root of a number is determined when a quantity of a number is produced when multiplied by itself or a factor of a number when multiplied by itself gives the original number.

In simple terms when a value is multiplied by itself it gives the original number. For a better understanding. The number 81 when multiplied by itself (9 × 9) = 81. The square root for  (81) is 9. 

The calculation for the square root of 32

To find the square root of any number first the given number is usually checked to determine whether they are a perfect square number or not. The square of the number s is found using the long division method.

For the number with a perfect square, it is easy to find the square roots and it is a bit tough for non-square values. Numbers like 4,9, 16,25, etc., are perfect squares. Numbers that end with 2,3,7 and 8 are not perfect square numbers.

Methods to find square root

There are three methods to find the square root of a number

  • Prime factorization method
  • Long division method
  • Repeated subtraction

These methods described above do not apply to finding the square root of any number.  

Steps to find the square root of 32

  • 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 32

  • Step 1: Find the smallest integer that can divide the number. 5 is the perfect root number that is smaller and closest to 32.
  • Step 2: Keep following the long division using divisor and dividend.
Long division method 
Long division method 
  • Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number. Hence, the √32 = 5.65

Solved examples

Q1: Find the square root of 4 using the prime factorization method
A1: Prime factors of 4 = 2×2
The √4 = 2

Q2: what is the square root of 2?

Long division method

A2:The √2 = 1.4142

Q3: What is the square root of 400 using repeated division

  1. 400 – 1 = 399
  2. 399 – 3 = 396
  3. 396 – 5 = 391
  4. 391 – 7 = 384
  5. 384 – 9 = 375
  6. 375 – 11 = 364
  7. 364 – 13 = 351
  8. 351 – 15 = 336
  9. 336 – 17 = 319
  10. 319 -19 = 300
  11. 300 – 21 = 279
  12. 279 – 23 = 256
  13. 256 – 25 = 231
  14. 231 – 27 = 204
  15. 204 – 29 = 175
  16. 175 – 31 =144
  17. 144 – 33 =111
  18. 111 – 35 = 76
  19. 76 – 37 = 39
  20. 39 – 39 = 0

A3: The √400 = 20.

Q4: What is the square root of 49
A4: The square root of 49 = 7

Example 5: What is the square root of 225
A5: The √225 = 15

Frequently asked questions

What is the √32?
The √32 = 5.65

Which method is used to find the √32
The standard method that is used to find the square root of any number is the long division method.

How to write the square root 32 in exponential form? 
321/2 or 320.5 is the exponential way to write √32

How to write the square root of 32 in radical form?
The radical form of writing square root is √32

Can I find the square root of 32 using other methods?
The other two methods are not applicable as 32 is not a perfect square number.

Is 32 an irrational number?
Yes, 32 is an irrational number since the number is not equal to zero.

What are the methods to find the square root of a number?
There are three methods to find the square root of a number:
Prime factorization method
Long division method
Repeated subtraction

Written by

Prerit Jain

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