## Square & Square Root of 484

Within the domain of algebraic mathematics, squares and square roots play pivotal roles. Squaring a number, like 484, involves multiplying it by itself, yielding 234256. This operation is foundational, crucial in exploring rational and irrational numbers. Understanding these basics enriches comprehension of mathematical relationships and patterns. Squares unveil inherent properties of numbers, while square roots unravel complex numerical mysteries. These concepts illuminate mathematical landscapes, guiding explorations into fractional territories. Mastery of squares and square roots empowers mathematicians to navigate diverse mathematical terrains, uncovering the elegance and complexity woven within algebraic frameworks.

## Square of 484

**484² (484 × 484) = 234256**

The square number 484 equals 234,256, derived by multiplying 484 by itself, showcasing a fundamental operation in algebraic mathematics and revealing inherent properties of numbers.

## Square Root of 484

**√484 = 22**

The square root of 484 is 22. This fundamental operation in mathematics uncovers the value that, when multiplied by itself, equals 484.

**Square Root of 484**: 22**Exponential Form:** 484^½ or 484^0.5**Radical Form**: √484

## Is the Square Root of 484 Rational or Irrational?

**Yes, the square root of 484 is a rational number.**

Rational Numbers: Rational numbers can be expressed as the quotient of two integers, where the denominator is not zero.

Irrational Numbers: Irrational numbers cannot be expressed as fractions of integers.

In essence, rational numbers can be expressed as fractions with finite or repeating decimals, whereas irrational numbers cannot be represented in this way, having non-repeating, non-terminating decimal expansions.

## Methods to Find the Value of Root 484

**Prime Factorization Method**: Break down 484 into its prime factors, which are 2 × 2 × 11 × 11. Since the square root of 484 is 22, it’s the product of the prime factors in pairs: (2 × 11) = 22.

**Long Division Method**: Use the long division algorithm to find the square root of 484 by approximation. Start with a guess (e.g., 20) and refine iteratively.

**Using a Calculator**: Most calculators have a square root function. Simply input 484 and find the square root directly.

**Estimation**: Since 484 is close to the perfect square of 400 (20 × 20) and 529 (23 × 23), you can estimate that its square root is likely between 20 and 23, closer to 22.

## Square Root of 484 by Long Division Method

**Step 1**: Pair the digits starting from the unit’s place and place a horizontal bar to indicate the pairing.**Step 2**: Find a number whose square is less than or equal to 4. Since 2 × 2 = 4, the quotient is 2.**Step 3**: Bring down 84 and multiply the quotient by 2, yielding 4. This becomes the starting digit of the new divisor.**Step 4**: Place 2 at the unit’s place of the new divisor. When 42 is multiplied by 2, we get 84. The answer obtained is 0.**Step 5**: Thus, the square root of 484 is 22.

## Is 484 a Perfect Square or Not?

**Yes, the number 484 is a perfect square.**

Yes, 484 is a perfect square because it can be expressed as the square of an integer, specifically (22 × 22), which equals 484. Therefore, the square root of 484 is a whole number (22), making it a perfect square.

## Is 484 a perfect cube?

No, 484 is not a perfect cube. The cube root of 484 is approximately 7.82, which is not an integer, indicating it cannot be expressed as the cube of an integer.

## What are the factors of 484?

The factors of 484 include 1, 2, 4, 11, 22, 44, 121, 242, and 484

## What is the prime factorization of 484?

The prime factorization of 484 is 2² × 11².

## Can the square root of 484 be negative?

Yes, the negative square root of 484 is -22, since (-22)² = 484.