What is the square root of 484?
20
22
24
26
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.
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.
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
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.
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.
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.
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.
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.
The factors of 484 include 1, 2, 4, 11, 22, 44, 121, 242, and 484
The prime factorization of 484 is 2² × 11².
Yes, the negative square root of 484 is -22, since (-22)² = 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.
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.
√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
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.
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.
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.
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.
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.
The factors of 484 include 1, 2, 4, 11, 22, 44, 121, 242, and 484
The prime factorization of 484 is 2² × 11².
Yes, the negative square root of 484 is -22, since (-22)² = 484.
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What is the square root of 484?
20
22
24
26
What is 484 when expressed as a perfect square?
22²
23²
24²
25²
What is the result when 484 is divided by its square root?
19
20
21
22
Which number squared gives 484?
20
22
24
26
What is the square of 22?
484
242
44
485
How do you find the square root of 484?
Multiply 484 by itself
Find the number which when squared equals 484
Add 484 to itself
Subtract 484 from 1000
If the square root of 484 is 22, what is 22 squared?
484
485
486
487
What is the relationship between 484 and 22?
484 is half of 22
484 is the square of 22
22 is the square of 484
22 is the cube root of 484
What is 484 divided by 11?
22
33
44
55
What is the result of multiplying 22 by itself?
445
484
545
578
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