Square Root of 119

The square root of 119 is 10.9087. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 119 is written as √119. 

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

The prime factorization of 119 breaks 119 into its prime numbers. 

The numbers 7 and 17 are the prime numbers 

Prime factorization of 119 is 7 × 17

Since 7 and 17 are not repeating, we can’t pair them

Therefore, √119 is expressed as √7 x √17, the simplest radical form
 

The long division method finds the square root of non-perfect squares.

Step 1: Write down the number 119

Step 2: Number 119 is a three-digit number, so pair them as (1), (19)

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 (19) 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 (19). Here, we can’t add any number after 2, because the number formed will be greater than 19.

Step 8: Subtract 19 from 2  → 19-2 =17. Now add a decimal point after the new quotient and adding two zeros will make it 1700

Step 9: Apply step 7 over here and continue the process until you reach 0.

Step 10: We can write  √119 as 10.9087

The approximation method finds the estimated square root of non-perfect squares.

Step 1: Identify the closest perfect square to 119. Numbers 100 and 121 are the closest perfect square to 119.

Step 2: We know that  √100 = 10 and  √121 = 11. Thus, we can say that  √119 lies between  10 and 11.

Step 3: Check if  √119 is closer to 10 or 11. Let us take 10.5 and 11. Since (10.5)² is 110.25 and (11)² is 121,  √119 lies between them.

Step 4: We can keep changing the values of 10.5 to 10. 6 and iterate the same process without changing 12 as the closest perfect square root.

The result of  √119 will be 10.9087
 

• 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.