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Square Root

What Is the Square Root of 49? How Do You Find the Square Root of 49?

Written by Prerit Jain

Updated on: 12 Aug 2023

What Is the Square Root of 49? How Do You Find the Square Root of 49?

What Is the Square Root of 49? How Do You Find the Square Root of 49?

The square root of 49 is 7. The square root of a number is the value when multiplied by itself giving the original number or the inversion of the square root is just squaring the number. Here the number given to us is 49. The root of 49 is 7, by squaring 72 we get 49. 

To find the square root of any number first know whether the number is a perfect square or not. The numbers that are perfectly square include 4, 9, 16, 25, and so on. The ones that are not perfect squares include 1,2,3,5 and so on. For those with a perfect square, the root square can be found easily.

For the ones that are not perfect squares, you can find the square root by using the long division method.  The number 49 is a perfect square number because when we find the square root of the number we get a whole integer and not the ones with decimals.

Methods to find the square root of 49

  • Prime factorization method
  • Repeated subtraction method
  • Long division method

Prime factorization method

Find the prime factors for the given numbers. If n is the prime factor, take the similar two numbers as n2.  Then multiply them we get the square root of the number. 

  • Step 1: Find the prime factors for the given number
    • 49 = 7 × 7
  • Step 2: Square the common factors
    • 49 = 72

There is no step 3 because there is only one common factor square.
Hence, √49 = 7.

Repeated subtraction method

Subtract the number with the first odd number, take the result, and start subtracting with the next odd number. Keep repeating the step until you reach zero. The step in which zero is obtained is the square root of the number.

  1. 49 – 1 = 48
  2. 48 – 3 = 45
  3. 45 – 5 = 40
  4. 40 – 7 = 33
  5. 33 – 9 = 24
  6. 24 – 11 = 13
  7. 13 – 13 = 0

The step in which we get zero is step 7. Hence, √49 = 7

Long division method

To find the square root using the long division method the integer or square digit that can divide the number is chosen and division is continued. 

Long Division Method
Long Division Method

Hence, √49 = 7

Solved examples

Example 1: The roots of  (49) and -(49) are the same says jack, what did you think?
Answer: The negative square has no real root.
49 has real roots while  – (49) has only imaginary roots.
Hence, they are not similar

Example 2: Riya wants to simply 49 to its simplest form, let’s help her.
Answer: 49 = 7 × 7
Hence the simplest form of  √49 = 7

Example 3: solve 449 + 349 
Answer: The √49 = 7
= 4 (7) + 3 (7)
= 28 + 21
= 49

Example 4: what is the value of x, if x49 = 21
Answer: x49 = 21
49 = 7
Hence, x*7 = 21
X = 21/7 = 3
Therefore x = 3.

Example 5: Find the perimeter of the square if the area of the square tile is 49.
Answer: The area of the tile = area = 49 = 7
The square tile has 4 sides therefore we multiply it by 4 = 4*7 = 28
Therefore the perimeter of the tile  = 28 units.

Frequently asked questions

What is the square root of 49?
The 49 = 7.

Is 49 a rational number?
Yes, 49 is a rational number because when we divide the number we get 7 and not 0 (p/q not= 0)

What is a perfect square number?
A perfect square number is one when we find the root of the number we get a whole number and not a decimal. 49 = 7 hence 49 is a perfect square number. 

What is the square root of 36?
The square root of 36 is
36 = 6

Manu bought 49 saplings, and he decided to plant them with the same number in rows and columns, how could he do that?
If Manu decides to plant equal numbers in both rows and columns then he must have squared them to find how much he should plant for them to be equal.
49 = 7
Therefore, Manu planted 11 plants in each row and column.

What is the square root of 49?
The square root of 49 = 7.

How to find the square root for irrational numbers?
To find the square root for irrational numbers use the long division method.

Written by

Prerit Jain

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