Square Root of 120

The square root of 120 is 10.954. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 120 is written as √120. 
 

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

The prime factorization of 120 breaks 120 into its prime numbers. 

The numbers 2, 3, and 5 are the prime numbers .

Prime factorization of 120 is 2³ × 3¹× 5^1.

Since 2 is repeating, we should pair them. We can’t pair 3 and 5 because they are not repeating.

Therefore, √20 is expressed as 2x√2 x √3 x√5, the simplest radical form.

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

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

Step 1: Write down the number 120

Step 2:  Number 120 is a three-digit number, so pair them as (1), (20)

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 (20) 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 (20). Here, we place 0 after 2, because the number formed will be greater than 20.

Step 8: Subtract 0 from 20  → 20-0 =20. Now add a decimal point after the new quotient and adding two zeros will make it 2000

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

Step 10: We can write  √120 as 10.954
 

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

Step 1: Identify the closest perfect square to 120. Numbers 100 and 121 are the closest perfect square to 120.

Step 2: We know that  √100 = 10 and  √121 = 11. Thus, we can say that  √120 lies between  10 and 11.

Step 3: Check if  √120 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,  √120 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  √120 will be 10.954
 

• 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.