Square root of 400

The square root of 400 is ±20. The positive value, 20 is the solution of the equation x² = 400. As defined, the square root is just the inverse of squaring a number, so, squaring 20 will result in 400.  The square root of 400 is expressed as √400 in radical form, where the ‘√’  sign is called the “radical”  sign. In exponential form, it is written as (400)^1/2  

We can find the square root of 400 through various methods. They are:

• Prime factorization method

• Long division method

• Subtraction method

The prime factorization of 400 involves breaking down a number into its factors. Divide 400 by prime numbers, and continue to divide the quotients until they can’t be separated anymore.

After factoring 400, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

So, Prime factorization of 400 = 2 × 2  × 2 × 2 × 5 × 5    

But for 400, two pairs of factor 2 and one pair of factors 5 can be obtained.

So, it can be expressed as  √400 = √(2 × 2  × 2 × 2 × 5 × 5) = 2 × 2 × 5 = 20

20 is the simplest radical form of √400

This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 400:

 Step 1: Write the number 400 and draw a bar above the pair of digits from right to left.

 Step 2: Now, find the greatest number whose square is less than or equal to 4. Here, it is 2 because 2²=4

Step 3: now divide 4 by 2 (the number we got from Step 2) such that we get 2 as a quotient, and we get a remainder.  Double the divisor 2, we get 4, and then the largest possible number A1=0 is chosen such that when 0 is written beside the new divisor 4, a 2-digit number is formed →40, and multiplying 0 with 40 gives 0, which is less than or equal to 0.

Repeat this process until you reach the remainder of 0. 

 
Step 4: The quotient obtained is the square root of 400. In this case, it is 20.

We know that the sum of the first n odd numbers is n². We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:

Step 1: take the number 400 and then subtract the first odd number from it. Here, in this case, it is 400-1=399

Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 399, and again subtract the next odd number after 1, which is 3, → 399-3=396. Like this, we have to proceed further.

Step 3: Now we have to count the number of subtraction steps it takes to yield 0 finally. 

Here, in this case, it takes 20 steps. 

So, the square root is equal to the count, i.e., the square root of 400 is ±20.

• Exponential form: An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent.Ex: 3 ⤬ 3 ⤬ 3 ⤬ 3 = 81 or, 3⁴ = 81, where 3 is the base, 4 is the exponent.

• Factorization: Expressing the given expression as a product of its factors Ex: 52=2 ⤬ 2 ⤬ 13 

• Prime Numbers : Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

• Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

• perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :2, 8, 18