Square Root of 484

The square root of 484 is 22. When a number is multiplied by itself, the resultant number is known as the square number and the number that is multiplied by itself is the square root. Read more on Square Root. Assuming 484 to be a perfect square number, we need to determine the square root of 484. We know that 2 × 2 = 4, so 20 × 20 = 400. But we need to find the square root of 484. So considering the square of 21, i.e. 21 × 21 = 441 and 22 × 22 = 484, we get the value of the square root of 484 as 22. This method of finding the square root of a number is called the estimation method. The other methods are detailed below. 

Note the Following:

The Square root of 484 = √484 = 2√484 where √ = radical, 484 is the radicand and 2 is the index.

Exponential Form of Square root of 484 = 484^1/2. 

Solution for √484 = 22

The square root of 484 is Irrational = False.

What is the Square root of 484?

The square root of 484 is 22, as the square root of 484 is a finite integer. 

How to Find the Square root of 484?

There are three methods to find the Square root of 484 

• Prime Factorisation method
• Long Division method
• Repeated Subtraction method

Square root of 484 by Prime Factorisation Method

The Prime Factorisation method, the number 484 is divided by prime divisors. The two same prime factors are grouped and removed from the root. The product of numbers out of the root forms the square root of 484. Steps mathematically shown below. 

484 = 2 × 2 × 11 × 11

√484 = √(2 × 2 × 11 × 11) = √(2 × 2) × √(11 × 11) 

Hence, √484 = 2 × 11 = 22.

Square root of 484 by Long Division Method

Let us try to find the square root of 484 using the long division method. The steps are

Step 1:  Grouping the given number into pairs. Say if the number is in the form ‘abc’, a and bc form the pairs.

Step 2: Consider the first number, which is “a”.

Let us find a square number that divides “a”

i.e 

1 × 1 = 1 

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16 and so on.

The division should be such that the multiples should be < or = to “a”

Step 3: Division to continue by including the next pair. ie, “bc”. 

Step 4: The first number to be used as the next divisor is (Divisor of first division + quotient of first division)

Step 5: New divisor would be the number from step 4 along with numbers from 1 to 9.

i.e., if the first divisor is d, then the new divisor would be 

d0 × 0 = 0

d1 × 1 = 

d2 × 2 = 

d3 × 3 = 

And so on.

Step 6: If the remainder is zero, then it is a perfect square and the quotient is the square root. Otherwise, the given number would be an imperfect square.

The detailed steps of 484 for long division is 

The remainder is zero and the division is complete. The quotient, which is 22, is the square root of the given number 484.

Square root of 484 by Repeated Subtraction Method.

In the repeated subtraction method, 484 is subtracted with odd numbers. If the subtraction results in zero, then 484 is a perfect square. Else 484 is not a perfect square.

The table below has the details of repeated subtraction for 484.

For the number 484 to be a perfect square with a rational root, the repeated subtraction should result in zero, which happens to be in step 22. Hence 22 is the square root of 484.

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Solved Examples

1. Which number that is smaller than 484 has a perfect square root?

441, which is less than 484, is a perfect square number. 21 is its perfect square root.

2. What is the square of 484?

234256 is the square of 484.