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Square Root of 484

The square of 22 gives 484. Hence, 484 is a perfect square number. The square root of 484 is a rational number. In this mini-lesson, we will learn to find the square root of 484 along with solved examples. Let us now find the square root of 484.

Square Root of 484: √484 = 22
Square of 484: 484² = 2,34,256

1.	What Is the Square Root of 484?
2.	Is Square Root of 484 Rational or Irrational?
3.	How to Find the Square Root of 484?
4.	FAQs on Square Root of 484

What Is the Square Root of 484?

On squaring 22, the number obtained is 484. Hence, the square root of 484 is 22. It is written as √484 = 22. Hence, 484 is a perfect square.

Is the Square Root of 484 Rational or Irrational?

As √484 = 22, it is possible to express √484 in p/q form easily. Hence, √484 a rational number.

How to Find the Square Root of 484?

There are different methods to determine the square root of any number. Click here to know more about it. Square root of 484 can be found using two methods:

Square Root of 484 by Long Division
Square Root of 484 by Prime Factorization

Square Root of 484 by Long Division

The square root of 484 can be found using the long division using the below given steps:

Step 1: First we will pair the digits of the given number starting with the unit's place. Place a horizontal bar to indicate the pairing.
Step 2: We will find a number which on multiplication with itself gives a product less than or equal to 4. We know that 2 × 2 = 4. Hence, the difference is 0 and the quotient is 2.
Step 3: Now, we have to bring down 84 and multiply the quotient by 2. This give us 4. Hence, 4 is the starting digit of the new divisor.
Step 4: 2 is placed at the unit's place of the new divisor because when 42 is multiplied by 2, we get 84. The answer obtained is 0.
Step 5: Hence, the square root of 484 is 22.

Square Root of 484 by Long Division Method

Square Root of 484 by Prime Factorization

484 can also be expressed as (2 × 2 × 11 × 11). The numbers which get repeated within the square root are 2 and 11. Hence, the square root of 484 is 2 × 11 = 22.

Thus, the square root of 484 is 22.

Explore square roots using illustrations and interactive examples

Important Notes:

484 is a perfect square number as the value obtained after taking its square root is a whole number.
The square root of 484 is simplified as 22 either by using the prime factorization of 484 or by expressing 484 as a square of 22.

Think Tank:

Can the value of square root of 484 be expressed as a decimal?
Are -√484 and √-484 same?

Example 1: What is the difference in lengths of square boxes having area 484 square inches and 400 square inches?

Solution

Area of a square box can be calculated using the formula = length × length
The length of the square box having area 484 square inches is √484 = 22 inches
Similarly, the length of the square box having area 400 square inches is √400 = 20 inches
The difference in lengths of the two boxes is (22 - 20) inches = 2 inches
Thus, the difference in length of the square boxes having area 484 square inches and 400 square inches is 2 inches.
Example 2: Is the radius of a circle of area 484π square inches less than 25 inches or more than 25 inches?

Solution

Radius can be found using the area of a circle formula, that is, πr². From the given information,

πr² = 484π
r² = 484

By taking the square root on both sides we get, √r²= √484. We know that the square root of r² is r. The square root of 484 is 22 inches. Hence, the radius of the circle of area 484π square inches is less than 25 inches.

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FAQs on Square Root of 484

What are the two square roots of 484?

The two square roots of 484 are -22 and +22.

Is 484 a perfect square?

Yes, 484 is a perfect square.

Does 484 have a square root?

Yes, 484 has a square root. The √484 is 22.

Can square root of 484 be simplified?

484 is broken down as the product of 2 × 2 × 11 × 11. The square root of 484 gives 22.

Is the square root of 484 rational or irrational?

The square root of 484 is rational.

Is the square root of 484 a real number?

Yes, the square root of 484 is a real number.

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