# Square & Square Root of 361

Created by: Team Maths - Examples.com, Last Updated: June 10, 2024

## Square of 361

361² (361×361) = 130321

The square of 361 is 130,321. It is obtained by multiplying 361 by itself. This number represents the area of a square with sides of length 361 units.

## Square Root of 361

√361 = 19

The square root of 361 is an important mathematical concept, representing the value that, when multiplied by itself, equals 361. This value is 19, as 19^2 equals 361. Unlike whole numbers, it is not irrational; it’s a perfect square, a whole number without decimal representation.

Square Root of 361: 19
Exponential Form: 361^½ or 361^0.5

## Is the Square Root of 361 Rational or Irrational?

The square root of 361 is an rational number.
• A rational number can be expressed as p/q, where p and q are integers and q is not zero. Rational numbers encompass integers, fractions, and terminating or repeating decimals.
• An irrational number is a real number that cannot be represented as the ratio of two integers. It cannot be written as a fraction where both the numerator and denominator are whole numbers.

The square root of 361 is an irrational number. It cannot be simplified into a fraction of two integers. Upon calculating the square root of 361, its decimal representation is non-repeating and non-terminating. This quality sets irrational numbers apart from rational numbers, which can be expressed as fractions. Falling outside the category of rational numbers, the square root of 361 is considered irrational due to its distinct decimal representation.

## Methods to Find Value of Root 361

1. Prime Factorization Method: Decompose 361 into its prime factors, then find the square roots of each prime factor and multiply them together.
2. Estimation Method: Begin with a range based on nearby perfect squares and refine guesses within this range until reaching a satisfactory approximation of √361.
3. Using Calculators or Software: Utilize calculators or mathematical software equipped with functions to compute the square root of 361 directly, providing accurate results.
4. Iteration Method: Employ iterative techniques like the Newton-Raphson method to iteratively refine initial guesses of √361 until achieving a desired level of precision.
5. Table Lookup: Refer to mathematical tables or online resources containing pre-calculated values of square roots to find an approximate value for √361.

## Square Root of 361 by Long Division Method

Let’s see how to find the square root of 361 using the long division method. Follow these steps:

1. 361 has 3 digits, so we put a bar on the first digit and another bar on the next pair of digits.
2. Look at the digit 3 with the bar. Find a number whose square is very close to and less than or equal to 3. Since 1 is such a number (if we take 2, 22 = 4, exceeding 3), we write 1 as the divisor and quotient.
3. Subtract as in normal division: 3 – 1 = 2. Carry forward the pair of digits, resulting in 61.
4. Double the existing divisor. Since the existing divisor was 1, doubling it gives 2, which we write in place of the new divisor.
5. Place the same digit in each blank of 2 _ × _ so that the product is very close to 261 and less than or equal to 261. We find that 29 × 9 = 261.
6. Subtract: 261 – 261 = 0.
7. Therefore, the square root of 361 is the number in the place of the quotient, which is 19. Hence, √361 = 19.

## 361 is Perfect Square Root or Not

Yes, 361 is a perfect square.

The square root of 361 is 19, making it a perfect square root. A perfect square root is an integer that, when multiplied by itself, yields the original number. In this case, 19 multiplied by 19 equals 361. Perfect square roots have rational values and are integral solutions to quadratic equations. They are distinct from non-perfect square roots, which result in irrational or non-integer values.

## FAQ’S

### Can the square root of 361 be negative?

Yes, the square root of 361 can be negative, yielding -19. This is because (-19) multiplied by itself equals 361

## What is the factorization of 361?

The factorization of 361 is 19 × 19, indicating that it is a perfect square.

## What is value of √ 361?

The square root of 361 is 19, as it represents the number that, when squared, equals 361.

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