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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
|1.||What is the Square Root of 32?|
|2.||Is the Square Root of 32 Rational or Irrational?|
|3.||How to Find the Square Root of 32?|
|5.||FAQs on Square Root of 32|
What is the Square Root of 32?
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
Is the Square Root of 32 Rational or Irrational?
The square root of 32 is an irrational number with non-terminating digits.
√32 = 5.65685424…
The square root of 60 can not be written in the form of p/q, hence it is an irrational number.
How to find the Square Root of 32?
There are 2 main methods we use to find the Square Root of 32-
- Prime Factorization
- Long division
There are other methods as well, more of which can be known by clicking here
- 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
Therefore, the Square Root of 3 is 5.656
- 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
- 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
Example 1: Kate wants to buy a square plot which is 32 miles² in area. She plans on fencing the area and wants to calculate the cost of doing so. If the cost per mile of fencing is $100, find the cost of fencing the entire perimeter of the plot?
- First, to calculate the cost of fencing we would need the perimeter of the land.
- To find the perimeter, we need to find the side length first.
- Side length is the square root of the area for a square.
- Therefore, the side length here will be √32 = 5.656, and the perimeter 4 times this.
- Therefore, the total cost of fencing = 4 × 5.656 × 100 = $2262.4
Example 2: What will be the distance covered by a car travelling at 4√2 miles per hour in 2 hours?
Solution: Distance covered = Speed × Time
Therefore, the car covers a total distance of 4√2 × 2 = 5.656 × 2 = 11.312 miles
FAQs on Square Root of 32
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 321/2.