# Square & Square Root of 49

Last Updated: July 29, 2024

## Square of 49

49² (49 × 49) = 2401

To calculate the square of 49, you multiply 49 by itself:

Therefore, the square of 49 is 2,401. This calculation is achieved by multiplying 49 by itself, resulting in 2,401. Understanding how to find the square number is crucial in various mathematical fields including algebra, geometry, and data analysis, as it provides a foundation for tackling more intricate problems and concepts.

## Square Root of 49

√49 = 7

This is because 7 × 7 = 49.

Thus, the square root of 49 is exactly 7. This calculation is important in various mathematical and practical contexts, such as geometry, where it can represent the side length of a square with an area of 49 square units. It’s also significant in algebra and engineering, where understanding square roots helps in solving problems involving areas and other applications that require precise measurements.

Square Root of 49: 7

Exponential Form: 49^½ or 49^0.5

## Is the Square Root of 49 Rational or Irrational?

The square root of 49 is rational.

The square root of 49 is rational because it equals 7, a whole number. Rational numbers include all integers, fractions, and decimals that can end or repeat. Since 7 is a clear, whole number, it’s definitely rational.

## Methods to Find Value of Root 49

Finding the square root of 49 can be approached through several methods. Here, we’ll explore some common techniques that help in determining the square root of this specific number effectively.

Prime Factorization
This method involves breaking down the number into its prime factors. Since 49 is equal to 7², it is clear that the square root is 7.

Using a Calculator
The most straightforward method to find the square root of any number, including 49, is by using a calculator. Simply inputting “√49” will immediately provide the answer, which is 7.

Long Division Method
This traditional method is useful for larger numbers but can also be applied to smaller ones like 49: Start by setting up 49 under the square root symbol.
Determine the largest number whose square is less than or equal to 49. Here, it’s evident that 7 x 7 equals 49.
The quotient obtained from this division will be the square root, which is 7.

Guess and Check Method
This involves estimating a number that, when squared, results in 49. Since 6² = 36 and 8² = 64 you can infer that the square root of 49 lies between 6 and 8. Refining your estimate to 7 confirms 7² = 49.

## Square Root of 49 by Long Division Method

To find the square root of 49 using the long division method, follow these steps:

Step 1: Digit Pairing
Starting from the right, pair up the digits of 49. Since 49 is a two-digit number, it is considered as one pair under a bar.

Step 2: Determine the Divisor and Quotient
Identify a number which, when squared, produces a result less than or equal to 49. The number 7 fits this requirement because 7×7=49. Set 7 as both the divisor and the quotient.

Step 3: Calculation and Verification
Subtract 7×7 from 49, which results in a remainder of 0. This confirms that there are no more digits to bring down and that 49 is a perfect square.

Thus, using the long division method, the square root of 49 is determined to be 7, demonstrating that 49 is indeed a perfect square.

## 49 is Perfect Square Root or Not

Yes, 49 is a perfect square.

The square root of 49 is 7, which is a whole number. Since 7 multiplied by itself results in 49 (7 × 7 = 49), 49 qualifies as a perfect square.

## Does 49 have 2 square roots?

Yes, 49 has two square roots. In mathematics, every positive number has two square roots: one positive and one negative. For the number 49, the positive square root is +7, and the negative square root is -7. This is because both 7 and -7, when squared, equal 49 ( 7² = 49) and (-7² =49) These two values are referred to as the principal square root (7) and its negative counterpart (-7).

## Which number is closest to the square root of 49?

The number closest to the square root of 49 is 7 itself, as it is the exact square root. The nearest integers are 6 and 8.

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