Square root of 1600

In this topic, the square root of 1600 is ±40. The square root of 1600 is expressed as √1600, in radical form. It is expressed as (1600)^½ in exponential form.
 

If a student wants to find the square root of a number. Which are the methods they can use?  Some common methods are,

• Prime factorization

• Long division

• Approximation

• Subtraction method 

Let’s check the square root of 1600 using these methods 
 

In this method, all the prime factors of the number are listed down and then from there one number from each pair is listed down. Then the numbers are multiplied together. 

By using prime factorization, let’s check out the square root of 1600.

Step 1: Listing out the prime factors of 1600 and pairing the same numbers.

Prime factors of 1600 = 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5

Pairing the factors i.e, (2 × 2), (2 × 2), (2 × 2), (5 × 5)

Step 2: multiplying a number from each pair

2 × 2 × 2 × 5 =40

Hence, the √1600 is 40
 

Here, the given number is divided into smaller numbers to find the square root of the number.

Using the long division method, let’s check the square root of 1600

Step 1: finding the number whose square is less than or equal to the 1600

 Here the number is 40, because 402 = 1600

Step 2: So, let’s divide 1600 by 40

Step 3: continue the process till the remainder is 0

The quotient will be the square root of the number.

Therefore, square root of 1600 is 40
 

Approximation method is mainly used for not a perfect square. As 1600 is a perfect square, the approximation method is not used to find the square root of 1600. 
 

In the subtraction method, based on the fact, the sum of the first n odd number is n2. So, here the given number is subtracted with the odd number starting with 1. The process will go on till the given number becomes 0. Here, the step count is equal to the square root of the number. 

Step 1: The given number is subtracted from 1, i.e, 1600 - 1 = 1599

Step 2: The obtained number is subtracted with the next odd number. Here, the number is 3, so 1599 - 3 =1596.

Step 3: Continue the process till the number is 0. Here the process will continue till step 40. Hence, the square root of 1600 is ±40.

1600 - 1 =1599  → step 1

1599 - 3 =1596  → step 2

1596 - 5 =1591  → step 3

1591 - 7 =1584  → step 4

1584 - 9 =1575  → step 5

1575 - 11 =1564  → step 6

1564 - 13 =1551  → step 7
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231 - 75 =156  → step 38

156 - 77=79      → step 39

79 - 79 =0          → step 40 
 

• Quotient: The result we got after dividing two numbers is the quotient

• Radical symbol: The radical symbol (√) is the symbol used to denote square root.

• Square of a number: The Square of a number is the product of the number when multiplied by itself.

• Prime factorization: It is the process of breaking down a number into prime numbers.