Last updated on May 26th, 2025
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.
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
We can find the square root of 36 through various methods. They are:
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
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.
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.
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.
Simplify √36 + √49 ?
√36 + √49
= 6 + 7
= 13
Answer : 13
firstly, we found the values of the square roots of 36 and 49, then added the values.
What is √36 multiplied by 2?
√36 ⤬ 2
= 6⤬2
= 12
Answer: 12
breaking √36 into the simplest form and multiplying by 2.
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.
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.
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
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
Find √36 / √6
√36/√6
= √(36/6)
=(√6 ╳ √6 )/√6
= √6
Answer : √6 ≅ 2.449
we first broke √36 into √6 ╳ √6 and then divided the product by √6 .
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
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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