313 LearnersLast updated on May 26th, 2025
Square Root of 147
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 147.
What is the Square Root of 147
The square root of 147 is ±12.124. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 147 is written as √147.
Finding the square root of 147
The different ways to find the square root of a number are prime factorization, long division and approximation/estimation method
Square root of 147 using prime Factorization Method
The prime factorization of 147 breaks 147 into its prime numbers.
The numbers 3 and 7 are the prime numbers
Prime factorization of 147 is 3 × 72
Since 7 is repeating, we can pair 7.
Therefore, √146 is expressed as 7√3, the simplest radical form
Square root of 147 using long division method
The long division method finds the square root of non-perfect squares.
Step 1: Write down the number 147
Step 2: Number 147 is a three-digit number, so pair them as (1), (47)
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 (47) 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 (47). Here, we place number 1 after 2, because the number formed is less than 47.
Step 8: Subtract 22 from 47 → 47-22 = 3. Now add a decimal point after the new quotient and adding two zeros will make it 300
Step 9: Apply step 7 over here and continue the process until you reach 0.
Step 10: We can write √147 as 12.124
Square root of 147 by Approximation method
The approximation method finds the estimated square root of non-perfect squares.
Step 1: Identify the closest perfect square to 147. Numbers 144 and 169 are the closest perfect square to 147.
Step 2: We know that √144 = 12 and √169 = 13. Thus, we can say that √147 lies between 12 and 13.
Step 3: Check if √147 is closer to 12 or 13. Let us take 12.5 and 13. Since (12.5)2 is 156.25 and (13)2 is 169, √147 lies between them.
Step 4: We can keep changing the values of 12.5 to 12. 6 and iterate the same process without changing 13 as the closest perfect square root.
The result of √147 will be 12.124
Common Mistakes and How to Avoid Them in Square Root of 147
Take a look at mistakes a child can make while finding the square root of 147:
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 √147 as 12.124.
Square Root of 147 Examples
Problem 1
Solve for y, if x² + y = 147 and x = √147
The value of y = 0
Explanation
When √147 is squared, the result will be 147, that is, x2 is 147. Apply this to the equation given, x2 + y to get the value of y as zero.
Problem 2
Find the difference between √169 and √147
The difference between √169 and √147 is 0.876
Explanation
Find the value of both square roots and take the difference. The value of √169 is 13 and the approximate value of √147 is 12.124. So, subtracting 12.124 from 169 will give 0.876 as the difference.
Problem 3
Find the decimal approximation of square root of 147 to the nearest hundredth
The approximate decimal value of square root of 147 will be 12.12
Explanation
The value of the square root of 147 is approximately 12.124. When we round off this value, we will get the value as 12.12.
FAQs on 147 Square Root
1.How do you simplify √147?
2.What is the cube root of 147?
3.What are the square factors of 147?
4.What is 147 divisible by?
5.What’s the square of 147?
6.How does learning Algebra help students in Qatar make better decisions in daily life?
7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 147?
8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 147?
9.Does learning Algebra support future career opportunities for students in Qatar?
Important Glossaries for Square Root of 147
- 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.
