Square root of 32

Before we begin, let's understand the meaning of the square root. The symbol square root is written as √ and is an integral part of mathematics. Once you understand the basics of finding the square root of a number, you can solve any square root-related problem. In this short lesson, we will learn about the square root of 32. 32 is not a perfect square number. Hence, the square root of 32 is an irrational number. We will be using methods like prime factorization and division, and learn how to find out the square root of 32. We will also focus on some solved examples based on square root of 32
Let us see what the square root of 32 is:

• Square Root of 32: √32 = 5.65685424...
• Square of 32: 32² = 1024

The square root of any number x can be written as √x. Let there be a number a such that x = a × a. Now it can also be written as: a² = x or a = √x . Therefore, a is called the second root of x.

• Now, if x = 32, then a = √32 is the square root of 32. In the simplest radical form, √32 = √(16 × 2) = 4√2
• The decimal form of √32 = 5.657

• Prime Factorization
• Long division

There are other methods as well, more of which can be known by clicking here

Prime Factorization

• To find the square root of 32, we shall first express it in terms of its prime factors.
  32 = 2 × 2 × 2 × 2 × 2. 
• Next, this can be reduced further to 
  32 = 16 × 2
• Finally, to find the root of this from here is very easy, 
  √32 = √(16 × 2)
  √32 = 4√2
  = 4 × 1.414
  = 5.656 

Therefore, the Square Root of 3 is 5.656

Long Division

• Step 1: Place a bar over 32. We also pair the 0s in decimals in pairs of 2 from left to right.
• Step 2: Find a number such that when you multiply it with itself, the product is less than or equal to 32.
  We know that 5 × 5 is 25 and is less than 32. Now let us divide 32 by 5
• Step 3: Let us place a decimal point and pairs of zeros and continue our division.
  Now, add the divisor 5 with itself and the sum becomes the starting digit of our next divisor.
• Step 4: Choose a number in the unit's place for the new divisor such that its product with the same number is less than or equal to 700.
  If we put a 6 in the one’s place, our product is less than 700. We get 106 × 6 = 636.
• We continue doing the same steps till we get the number of decimals we require.

So our long division now looks like this:

Explore Square Roots using illustrations and interactive examples

• Square Root of 36
• Square Root of 16
• Square Root of 2
• Square Root of 34
• Square Root of 8

• The square root of 32 ≈ 5.656
• The square root of 32 in its simplest radical form is 4√2
• √32 is irrational. Its real roots are +5.656 and -5.656

What is the square root of 32?

The square root of 32 is √32 = 5.656

What is the square of 32?

The square of 32 is 32² = 1024

What is the square root of 32 simplified?

The square root of 32 in simplified form is 4√2.

Is the square root of 32 a rational number?

The square root of 32 is an irrational number as it is non-terminating. It cannot be expressed in the form p/q which is what makes a rational number.

What is the exponent form of root 32?

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