269 LearnersLast updated on May 26th, 2025
Square Root of 149
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 149.
What is the Square Root of 149
The square root of 149 is ±12.206. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 149 is written as √149.
Finding the square root of 149
The different ways to find the square root of a number are prime factorization, long division and approximation/estimation method
Square root of 149 using prime Factorization Method
The prime factorization of 149 breaks 149 into its prime numbers.
The number 149 is the only prime number.
Prime factorization of 149 is 1491
Since 149 is not repeating, we can’t pair them.
Therefore, √149 is expressed as √149 itself
Square root of 149 using long division method
The long division method finds the square root of non-perfect squares.
Step 1: Write down the number 149
Step 2: Number 149 is a three-digit number, so pair them as (1), (49)
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 (49) 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 (49). Here, we place the number 2 after 2, because the number formed is less than 49.
Step 8: Now multiply the quotient 2 with 22 to get 44. Subtract 44 from 49 → 49 - 44 = 5. Now add a decimal point after the new quotient and adding two zeros will make it 500.
Step 9: Apply step 7 over here and continue the process until you reach 0.
Step 10: We can write √149 as 12.206
Square root of 149 by Approximation method
The approximation method finds the estimated square root of non-perfect squares.
Step 1: Identify the closest perfect square to 149. Numbers 144 and 169 are the closest perfect square to 149.
Step 2: We know that √144 = 12 and √169 = 13. Thus, we can say that √149 lies between 12 and 13.
Step 3: Check if √149 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, √149 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 √149 will be 12.206
Common Mistakes and How to Avoid Them in Square Root of 149
Take a look at mistakes a child can make while finding the square root of 149:
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 √149 as 12.206.
Square Root of 149 Examples
Problem 1
Calculate the area of circle if ‘r’ = √149
The area of the circle is 467.86 square units
Explanation
The area of the circle can be calculated using the formula πr2. Here π = 31.4 and we need to find r2. According to the formula, area of circle = πr2=
3.14 ×(√149)2 = 3.14 × 149 = 467.86 square units.
Problem 2
Compare the powers of square roots (√149)²and (√250)² to identify the greatest square root.
The greatest square root will be (√250)2
Explanation
When both the square roots get squared, we get the results as 149 and 250. Among these 250 is the biggest. So (√250)2 is the greatest square root.
Problem 3
Find the value of √149 +√20
The value is 13
Explanation
First add root 149 and root 20 to get √169. To simplify it, take the square root of √169, which is 13. So, the final answer is 13.
FAQs on 149 Square Root
1.How can we apply square roots in real-life?
2.What is the perfect square of 149?
3.Identify the biggest factor of 149
4.Which method is best for square roots with irrational numbers?
5.Express 149 using prime factorization method
6.How does learning Algebra help students in Thailand make better decisions in daily life?
7.How can cultural or local activities in Thailand support learning Algebra topics such as Square Root of 149?
8.How do technology and digital tools in Thailand support learning Algebra and Square Root of 149?
9.Does learning Algebra support future career opportunities for students in Thailand?
Important Glossaries for Square Root of 149
- 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.
