Last updated on May 26th, 2025
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.
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.
The different ways to find the square root of a number are prime factorization, long division and approximation/estimation 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
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
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
Take a look at mistakes a child can make while finding the square root of 135:
Determine whether √135 < √144
Yes, √135 < √144
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.
Prove that √135 + √169 is irrational
The sum of √135 + √169 is 24.616, making it irrational
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.
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.
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.
The area of a circle of 135 cm² . Calculate the radius.
The radius of circle will be 6.53 cm
The area of the circle = πr² → 135 = 3.14 × r2 → r = √135/3.14 = 6.53.
The value of π is 3.14.
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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