Square Root of 150
2026-02-28 21:42 Diff
https://brightchamps.com/en-us/math/algebra/square-root-of-150

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Last updated on August 5, 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 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

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
 

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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:
 

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Problem 1

Calculate the volume of a cube, if s = √150

Okay, lets begin

 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
 

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Problem 2

Simplify (√150 + √150) / 2

Okay, lets begin

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.
 

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Problem 3

What is √150 when 5 is added?

Okay, lets begin

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
 

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FAQs on 150 Square Root

1.Is 150 a perfect square root?

No, 150 is a not a perfect square root because the value of square root is not a whole number. 
 

2.What is √150 between?

√150 is between √144 and √169. The square root of √144 is 12 and √169 is 13

3.What is 150 square root nearest integer?

The nearest integer to 150 square root is 12. Since the approximate value of the square root of 150 is ±12.25, (rounded value), 12 is the nearest integer.

4.Is √150 irrational?

Yes, √150 is irrational because the value of the square root is decimal and cannot be expressed as a proper fraction.
 

5.What are the multiples of 150?

The multiples of 150 are 150, 300, 450, 600,750 and so on.

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

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.