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. 
 

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

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

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
 

• 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.