301 LearnersLast updated on May 26th, 2025
Square Root of 135
Square root is the number obtained when a number is multiplied with itself. We apply the concept of square root in architecture, to measure volume and surface area. In this article, we’ll learn how to find the square root of 135.
What is the Square Root of 135
The square root of 135 is ±11.618. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 135 is written as √135.
Finding the square root of 135
The different ways to find the square root of a number are prime factorization, long division and approximation/estimation method
Square root of 135 using prime Factorization Method
The prime factorization of 135 breaks 135 into its prime numbers.
The numbers 3 and 5 are the prime numbers
Prime factorization of 135 is 33 × 5
Since 3 and 5 are not repeating, we can’t pair them
Therefore, √135 is expressed as 3√3√5, the simplest radical form
Square root of 135 using long division method
The long division method finds the square root of non-perfect squares.
Step 1: Write down the number 135
Step 2: Number 135 is a three-digit number, so pair them as (1), (35)
Step 3: Find the largest that is closest to the first pair (1), which is 12
Step 4: Write down 1 as the quotient, which will be the first digit of the square root.
Step 5: Subtracting 12 from 1 will leave zero as the remainder. Now bring down the second pair (35) and place it beside 0.
Step 6: Now double the quotient you have, that is multiply the quotient 1 with 2 and the result will be 2
Step 7: Choose a number such that it can be placed after 2. The two-digit number created should be less than the second pair (35). Here, we place number 1 after 2, because the number formed is less than 35.
Step 8: Subtract 21 from 35 → 35-21 = 14. Now add a decimal point after the new quotient and adding two zeros will make it 1400
Step 9: Apply step 7 over here and continue the process until you reach 0.
Step 10: We can write √135 as 11.618
Square root of 119 by Approximation method
The approximation method finds the estimated square root of non-perfect squares.
Step 1: Identify the closest perfect square to 135. Numbers 121 and 144 are the closest perfect square to 135.
Step 2: We know that √121 = 11 and √144 = 12. Thus, we can say that √135 lies between 11 and 12.
Step 3: Check if √135 is closer to 11 or 12. Let us take 11.5 and 12. Since (11.5)2 is 132.25 and (12)2 is 144, √135 lies between them.
Step 4: We can keep changing the values of 11.5 to 11. 6 and iterate the same process without changing 12 as the closest perfect square root.
The result of √135 will be 11.616
Common Mistakes and How to Avoid Them in Square Root of 135
Take a look at mistakes a child can make while finding the square root of 135:
Mistake 1
Trying to guess the square root instead using the methods
Finding square roots for non-perfect squares without using the method is time-consuming. Always use the long division method to find the square root of non-perfect squares. Using the long-division method, we can find √135 as 11.616.
Mistake 2
Misunderstanding the square root of 135 with the division
A kid might divide 135 by 2, assuming that the result will give the square root. Understand the difference between finding a square root and dividing a number. A square root is the number that gets multiplied two times.
Mistake 3
Calculation mistake in subtracting the digits
Always be sure that you have checked the arithmetic calculations. If you subtract the digits incorrectly, the square root you get will also be incorrect.
Square Root of 135 Examples
Problem 1
Determine whether √135 < √144
Yes, √135 < √144
Explanation
Take the values of both √135 and √144. Compare the value to determine whether √135 < √144. The value for √135 is 11.616 and √144 is 12. Hence, we can say that √135 < √144.
Problem 2
Prove that √135 + √169 is irrational
The sum of √135 + √169 is 24.616, making it irrational
Explanation
Irrational numbers are numbers that cannot be expressed as a proper fraction. The value of √135 is 11.616 and value of √169 is 13. Adding them will give 24.616 as the sum.
Problem 3
The hypotenuse of a triangle is 13 cm, length of one side is 5 cm. What will be the length on the other side?
The length of the other side will be 12 cm.
Explanation
Apply the Pythagoras theorem. According to the formula, a2 + b2 = c2,
where a = 5, b = ?, and c = 13.
Therefore, a2 + b2 = c2 → 52 + b2 = 132 → 25 + b2 = 169.
Therefore, b2 = 169 - 25 = 144 → b = √144 = 12.
Problem 4
The area of a circle of 135 cm² . Calculate the radius.
The radius of circle will be 6.53 cm
Explanation
The area of the circle = πr² → 135 = 3.14 × r2 → r = √135/3.14 = 6.53.
The value of π is 3.14.
FAQs on 135 Square Root
1.Is 135 a perfect square?
2.Is 135 a cube root?
3.What are the factors of 135?
4.Is 135 a multiple of 9?
5.Can 135 be divided by 2?
6.How does learning Algebra help students in India make better decisions in daily life?
7.How can cultural or local activities in India support learning Algebra topics such as Square Root of 135?
8.How do technology and digital tools in India support learning Algebra and Square Root of 135?
9.Does learning Algebra support future career opportunities for students in India?
Important Glossaries for Square Root of 135
- Perfect Square: Product obtained when the same number gets multiplied twice
- Approximate Value: Value closer to the exact number
- Prime Factorization: Breaking down the number into its prime factors.
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Jaskaran Singh Saluja
About the Author
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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
