Square Root of 130

The square root of 130 is ±11.4018. Finding the square root of a number is the inverse process of finding the perfect square. The square root of 130 is written as √130. 
 

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

The prime factorization of 130 breaks 130 into its prime numbers. 

The numbers 2, 5 and 13 are the prime numbers 

Prime factorization of 130 is 2 × 5 × 13

Since 2, 5 and 13 are not repeating, we can’t pair them

Therefore, √119 is expressed as √2 x √5 x √13, the simplest radical form

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

Step 1: Write down the number 130

Step 2: Number 130 is a three-digit number, so pair them as (1), (30)

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 (30) and place it beside 0.

Step 6: Now double the quotient you have, that is added 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 (30). Here, we number 1 after 2, because the number formed will be less than 30.

Step 8: Subtract 21 from 30 → 30-21 =9. Now add a decimal point after the new quotient and adding two zeros will make it 900

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

Step 10: We can write  √30 as 11.4017
 

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

Step 1: Identify the closest perfect square to 130. Numbers 121 and 144 are the closest perfect square to 130.

Step 2: We know that  √121 = 11 and  √144 = 12. Thus, we can say that √130 lies between  11 and 12.

Step 3: Check if  √130 is closer to 11 or 12. Let us take 11.5 and 12. Since (11.5)² is 132.25 and (12)² is 144,  √130 lies between them.

Step 4: We can keep changing the values of 11.5 to 11. 6 and iterate the same process without changing 12 as the closest perfect square root.

The result of  √130 will be 11.4017
 

• 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.