259 LearnersLast updated on May 26th, 2025
Square Root of 150
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 150.
What is the Square Root of 150
The square root of 150 is ±12.247. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 150 is written as √150.
Finding the square root of 150
The different ways to find the square root of a number are prime factorization, long division and approximation/estimation method
Square root of 150 using prime Factorization Method
The prime factorization of 150 breaks 150 into its prime numbers.
The numbers 2, 3 and 5 are the prime numbers
Prime factorization of 150 is 21 × 31 × 52
Only 5 is repeating here, so we can pair 5 but not 2 and 3
Therefore, √150 is expressed as 5 x √2 x √3
Square root of 150 using long division method
The long division method finds the square root of non-perfect squares.
Step 1: Write down the number 150
Step 2: Number 150 is a three-digit number, so pair them as (1), (50)
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 (50) 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 (50). Here, we place the number 2 after 2, because the number formed is less than 50.
Step 8: Now multiply the quotient 2 with 22 to get 44. Subtract 44 from 50 → 50 - 44 = 6. Now add a decimal point after the new quotient and adding two zeros will make it 600
Step 9: Apply step 7 over here and continue the process until you reach 0.
Step 10: We can write √150 as 12.247
Square root of 150 by Approximation method
The approximation method finds the estimated square root of non-perfect squares.
Step 1: Identify the closest perfect square to 150. Numbers 144 and 169 are the closest perfect square to 150.
Step 2: We know that √144 = 12 and √169 = 13. Thus, we can say that √150 lies between 12 and 13.
Step 3: Check if √150 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, √150 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 √150 will be 12.247
Common Mistakes and How to Avoid Them in Square Root of 150
Take a look at mistakes a child can make while finding the square root of 150:
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 √150 as 12.247.
Square Root of 150 , Examples
Problem 1
Calculate the volume of a cube, if s = √150
The volume of the cube is 1837.05 m3.
Explanation
To find the volume of a cube, we use the formula s3.
Here, s = √150
Therefore, s3 = (√150)3
= (√150)2 x √150
= 150 x √150
= 150 × 12.247
= 1837.05 m3
Problem 2
Simplify (√150 + √150) / 2
The result is 12.247
Explanation
The approximate value of √150 is 12.247. So, √150 + √150 = 12.247 + 12.247 = 24.494. Now divide 24.494 by 2 to get the final result. Dividing 24.494 by 2 gives 12.247.
Problem 3
What is √150 when 5 is added?
The result is 17.247
Explanation
The approximate value of √150 is 12.247. When 5 is added to it, we get the result 17.247
FAQs on 150 Square Root
1.Is 150 a perfect square root?
2.What is √150 between?
3.What is 150 square root nearest integer?
4.Is √150 irrational?
5.What are the multiples of 150?
6.How does learning Algebra help students in United States make better decisions in daily life?
7.How can cultural or local activities in United States support learning Algebra topics such as Square Root of 150?
8.How do technology and digital tools in United States support learning Algebra and Square Root of 150?
9.Does learning Algebra support future career opportunities for students in United States?
Important Glossaries for Square Root of 150
- 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 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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