331 LearnersLast updated on May 26th, 2025
Square root of 36
The square root of 36 is the inverse operation of squaring a value “y” such that when “y” is multiplied by itself → y × y, the result is 36. It contains both positive and a negative root, where the positive root is called the principal square root.
What Is the Square Root of 36?
The square root of 36 is ±6. The positive value, 6 is the solution of the equation x2 = 36. As defined, the square root is just the inverse of squaring a number, so, squaring 6 will result in 36. The square root of 36 is expressed as √36 in radical form, where the ‘√’ sign is called the “radical” sign. In exponential form, it is written as (36)1/2
Finding the Square Root of 36
We can find the square root of 36 through various methods. They are:
- Prime factorization method
- Long division method
- Subtraction method
Square Root of 36 By Prime Factorization Method
The prime factorization of 36 involves breaking down a number into its factors. Divide 36 by prime numbers, and continue to divide the quotients until they can’t be separated anymore.
After factoring 36, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs.
So, Prime factorization of 36 = 2 × 2 × 3 × 6
But for 36, pairs of factor 2 and 3 can be obtained.
So, it can be expressed as √36 = √(2 × 3 × 2 × 3) = 2 × 3=6
6 is the simplest radical form of √36
Square Root of 36 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 36:
Step 1: Write the number 36 and draw a bar above the pair of digits from right to left. 36 is a 2-digit number, so it is already a pair.
Step 2: Now, find the greatest number whose square is less than or equal to 36. Here, it is 6 Because 62=36.
Step 3: Now divide 36 by 6 (the number we got from Step 2) and we get a remainder of 0.
Step 4: The quotient obtained is the square root. In this case, it is 6.
Square Root of 36 By Subtraction Method
We know that the sum of the first n odd numbers is n2. We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:
Step 1: take the number 36 and then subtract the first odd number from it. Here, in this case, it is 36-1=35
Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 35, and again subtract the next odd number after 1, which is 3, → 35-3=32. Like this, we have to proceed further.
Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 6 steps.
So, the square root is equal to the count, i.e., the square root of 36 is ±6.
Common Mistakes and How to Avoid Them in the Square Root of 36
When we find the square root of 36, 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
Incorrectly applying the square root property.
Square roots do not distribute over additions. For example, √36 ≠ √10 + √26
Mistake 2
Ignoring precision
Provide an approximate answer without acknowledging the extent of precision is not expected.
Mistake 3
Not noticing that the square root of 36 is related to the square root of 4 and 9.
Notice that √36 can be broken into √(4⤫6) which assists to get the result easily.
Mistake 4
Incorrect formula for finding square roots through different methods.
The formula should be applied accurately for iterative methods.
Mistake 5
Rounding √36 too early and not able to get precision.
Regulate decimal places as needed. For example, if needed to have correct up to 2 decimal places, we can keep the value as 6.00.
Square Root of 36 Examples
Problem 1
Simplify √36 + √49 ?
√36 + √49
= 6 + 7
= 13
Answer : 13
Explanation
firstly, we found the values of the square roots of 36 and 49, then added the values.
Problem 2
What is √36 multiplied by 2?
√36 ⤬ 2
= 6⤬2
= 12
Answer: 12
Explanation
breaking √36 into the simplest form and multiplying by 2.
Problem 3
Find the radius of a circle whose area is 36π cm^2.
Given, the area of the circle = 36π cm2
Now, area = πr2 (r is the radius of the circle)
So, πr2 = 36π cm2
We get, r2 = 36 cm2
r = √36 cm
Putting the value of √36 in the above equation,
We get, r = ±6 cm
Here we will consider the positive value of 6.
Therefore, the radius of the circle is 6 cm.
Answer: 6 cm.
Explanation
We know that, area of a circle = πr2 (r is the radius of the circle) .According to this equation, we are getting the value of “r” as 6 cm by finding the value of the square root of 36.
Problem 4
Find the length of a side of a square whose area is 36 cm^2
Given, the area = 36 cm2
We know that, (side of a square)2 = area of square
Or, (side of a square)2 = 36
Or, (side of a square)= √36
Or, the side of a square = ± 6.
But, the length of a square is a positive quantity only, so, the length of the side is 6 cm.
Answer: 6 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 5
Find √36 / √6
√36/√6
= √(36/6)
=(√6 ╳ √6 )/√6
= √6
Answer : √6 ≅ 2.449
Explanation
we first broke √36 into √6 ╳ √6 and then divided the product by √6 .
FAQs on Square Root of 36
1.What is the √36 in fraction?
2.Is √36 a natural number?
3.Is 36 a perfect square or non-perfect square?
4.Is the square root of 36 a rational or irrational number?
5. Does 36 have two square roots?
6.How does learning Algebra help students in Bahrain make better decisions in daily life?
7.How can cultural or local activities in Bahrain support learning Algebra topics such as Square root of 36?
8.How do technology and digital tools in Bahrain support learning Algebra and Square root of 36?
9.Does learning Algebra support future career opportunities for students in Bahrain?
Important Glossaries for Square Root of 36
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: 3 ⤬ 3 ⤬ 3 ⤬ 3 = 81 Or, 3 4 = 81, where 3 is the base, 4 is the exponent
Factorization: Expressing the given expression as a product of its factors Ex: 52=2 ⤬ 2 ⤬ 13
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 :2, 8, 18
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