335 LearnersLast updated on May 26th, 2025
Square Root of 32
The square root of 32 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 32. The number 32 has a unique non-negative square root, called the principal square root.
What Is the Square Root of 32?
The square root of 32 is ±5.656854… . Finding the square root is just the inverse of squaring a number and hence, squaring 5.656854… will result in 32. The square root of 32 is written as √32 in radical form. In exponential form, it is written as (32)1/2
Finding the Square Root of 32
We can find the square root of 32 through various methods. They are:
- Prime factorization method
- Long division method
- Approximation/Estimation method
Square Root of 32 By Prime Factorization Method
The prime factorization of 32 is done by dividing 32 by prime numbers and continuing to divide the quotients until they can’t be divided anymore.
- Find the prime factors of 32
-
After factorizing 20, make pairs out of the factors to get the square roo
If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs.
So, Prime factorization of 32 = 2 × 2 × 2 × 2 × 2
But here in case of 32, two pairs of factor 2 can be obtained and a single 2 is remaining
So, it can be expressed as √32 = 2 × 2 ×√2 = 4√2
4√2 is the simplest radical form of √32
Square Root of 32 By Long Division Method
This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.
Follow the steps to calculate the square root of 32:
Step 1: Write the number 32, and draw a horizontal bar above the pair of digits from right to left.
Step 2: Now, find the greatest number whose square is less than or equal to 32. Here, it is
5, Because 52=25 < 32.
Step 3: Now divide 32 by 5 (the number we got from Step 2) such that we get 5 as quotient
and then multiply the divisor with the quotient, we get 25
Step 4: Subtract 25 from 32. Add a decimal point after the quotient 5, and bring down two zeroes and place it beside the difference 7 to make it 700.
Step 5: Add 5 to same divisor, 5. We get 10.
Step 6: Now choose a number such that when placed at the end of 10, a 3-digit number will be formed. Multiply that particular number by the resultant number to get a number less than 700. Here, that number is 6.
106×6=636<700.
Step 7: Subtract 700-636=64. Again, bring down two zeroes and make 64 as 6400. Simultaneously add the unit’s place digit of 106, i.e., 6 with 106. We get here, 112. Apply Step 5 again and again until you reach 0.
We will show two places of precision here, and so, we are left with the remainder, 77500 (refer to the picture), after some iterations and keeping the division till here, at this point
Step 8 : The quotient obtained is the square root. In this case, it is 5.65….
Square Root of 32 By Approximation
Approximation or estimation of square root is not the exact square root, but it is an estimate.
Here, through this method, an approximate value of square root is found by guessing.
Follow the steps below:
Step 1: Find the nearest perfect square number to 32. Here, it is 25 and 36.
Step 2: We know that, √25=5 and √36=6. This implies that √32 lies between 5 and 6.
Step 3: Now we need to check √32 is closer to 5 or 6. Let us consider 5.5 and 6. Since (5.5)2=30.25 and (6)2=36.
Thus, √32 lies between 5.5 and 6.
Step 4: Again considering precisely, we see that √32 lies close to (5.5)2=30.25. Find squares of (5.6)2=31.36 and (5.8)2= 33.64.
We can iterate the process and check between the squares of 5.62 and 5.7 and so on.
We observe that √32=5.65…
Common Mistakes and How to Avoid Them in the Square Root of 32
When we find the square root of 32, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.
Mistake 1
Misunderstanding symbol
Often when √32 is mistaken as 322 , we square the number 32 and get the result as 1024. So, understanding of symbol should be clear
Square Root of 32 Examples
Problem 1
if x= √32, what is x^2-2 ?
x= √32
⇒ x2 = 32
⇒ x2-2 = 32-2
⇒ x2-2 = 30
Answer : 30
Explanation
we did the square of the given value of x and then subtracted 2 from it.
Problem 2
Find the length of a side of a square whose area is 32 cm^2 ?
Given, the area = 32 cm2
We know that, (side of a square)2 = area of square
Or, (side of a square)2 = 32
Or, (side of a square)= √32
Or, side of a square = ±5.656
But, length of a square is a positive quantity only, so, length of the side is 5.656 cm.
Answer: 5.656 cm
Explanation
We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its Square root is the measure of the side of the square
Problem 3
Simplify (√32 + √32) × √32
√32 + √32) × √32
= (5.656 + 5.656) × 5.656
= 11.312 × 5.656
= 63.980672
Answer: 63.980672
Explanation
We first solved the part inside the brackets, i.e., √32 + √32, which resulted into 11.312 and then multiplying it with √32 which is 5.656 we get 63.980672
Problem 4
Simplify 5√32 + 13√32 ?
5√32+13√32
= √32(5+13)
= 5.65 × (5+13)
=18 × 5.65 = 101.7
Answer : 101.7
Explanation
Taking out the common part √32, adding the values inside bracket. √32= 5.65, so multiplying the square root value with the sum.
Problem 5
Calculate (√32/4 + √32/2)
√32/4 + √32/2
= 5.656/ 4 + 5.656/2
= 1.414 + 2.828
= 4.242
Answer : 4.242
Explanation
From the given expression, we first found the value of square root of 32 then solved by simple divisions and then simple addition.
FAQs on 32 Square Root
1.Is the square root of 32 a real number?
2.What is the cube root of 32?
3.Is 32 a perfect square or non-perfect square?
4.Is the square root of 32 a rational or irrational number?
5. How to find the square root of 33?
6.How does learning Algebra help students in Saudi Arabia make better decisions in daily life?
7.How can cultural or local activities in Saudi Arabia support learning Algebra topics such as Square Root of 32?
8.How do technology and digital tools in Saudi Arabia support learning Algebra and Square Root of 32?
9.Does learning Algebra support future career opportunities for students in Saudi Arabia?
Important Glossaries for Square Root of 32
- Exponential form: An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 2 4 = 16, where 2 is the base, 4 is the exponent
- Prime Factorization: Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3
- Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....
- Rational numbers and Irrational numbers:The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.
- Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24
- Decimal places: It is defined as the digits that appear to the right of the decimal point. Ex- the value of the square root of 32 rounded to 2 decimal places is 5.65
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Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
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