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. 
 

The different ways to find the square root of a number are prime factorization, long division  and approximation/estimation 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
 

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
 

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
 

• 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.