Square Root of 32

Square Root of 32 is approximately equal to 5.65685424… So on. Here, 5.65685424 is the number which when multiplied by itself will give the product approximately equal to 32. The expression for the square root of 32 is √32, where the radical sign is “√” and the radicand is 32. We shall discover the several approaches to calculating the square root of 32 in this article.

What is Square Root of 32?

Square Root of the number 32 can be written as √32. Square Root or simply the root of 32 is 5.656… This signifies that when 5.6568² = 32.

• In the decimal form of √32 = 5.657
• In the simplest radical form, √32 = √(16 × 2) = 4√2
• Fractional Exponent Form, (32)^1/2 = 5.656…

Square Root Calculator

Try out the following calculator to find the square root of 32

How to Calculate a Square Root of 32?

Square Root of 32 can be calculated using the following methods:

• Long Division Method
• Prime Factorization Method

Square Root of 32 by Long Division Method

The following procedures must be followed to determine the square root of 32:

Step 1: As here we start with the number 32 and use decimal points with the pairing of zeroes.

Step 2: Choose a perfect square less than 32 as the initial dividend 25. Hence divisor will be 5.

Step 3: Since the divisor is 5, the quotient is 5 therefore dividend will be 32. Subtract 25 from 32 and add 5 in the divisor.

Step 4: The new divisor is 10, the dividend is 7. Now put decimal after 5 in quotient and bring down two zeros. Therefore new dividend is 700.

Step 5: Add a digit at the left of 6 in the divisor i.e. at the unit place and also place the same digit in the quotient such that the product is near to 700.

Step 6: Add 6 in the divisor using step 5 hence, the new dividend will be 106 × 6 = 636. Subtract 636 from 700.

Step 7: This process should be repeated until the square root of 32 is found in three decimal places.

Therefore, the value of the square root of 32 approximately will be 5.6568.. so on.

Learn, Square Root by Long Division Method

Square Root of 32 by Prime Factorization

Prime Factorization of 32 is 32 = 2 × 2 × 2 × 2 × 2.

• Prime Factorization of 32 can be expressed as 2 × 2 × 2 × 2 × 2 or 2⁵
• Further, it can be reduced to 32 = 16 × 2.
• Now, For finding the root;
  √32 = √(16 × 2)
  √32 = 4√2
  = 4 × 1.414
  = 5.656
• Therefore the square root of 32 is 5.656 or 4√2.

Is Square Root of 32 Rational or Irrational?

The square root of 32 is an irrational number with non-terminating digits.

√32 = 5.65685424…So on

Therefore, the square root of 60 can not be written in the form of p/q, and it is never-ending, that continues after the decimal point too. So, the square root of 60 is an irrational number.

Square Root of 32 Value – FAQs

What is the Root of 32?

The square root or root of 32 approximate value is 5.6568.

What is the square of 32?

The square of 32 is 32² = 1024

Is √32 a Rational Number?

No, √32 is not a rational number.

Is 32 a Prime Number?

No, 32 is not a prime number because it’s evenly divided by other integers as well.

What is the Exponent Form of Root 32?

The exponent form if root 32 is 32^1/2

Is 32 a Perfect Square?

No, 32 is not a perfect square as its square root is not an integer.

Is -5.6568.. is a Square Root of 32?

Yes, -5.6568.. is also a square root of 32 as when -5.6568.. multiplied by itself give the product approximately equal to 32