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Square Root

What Is The Square Root of 169? How To Find The Square Root of 169?

Written by Prerit Jain

Updated on: 17 Aug 2023

What Is The Square Root of 169? How To Find The Square Root of 169?

What Is The Square Root of 169? How To Find The Square Root of 169?

The square root of 169 is 13. 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 169. The root of 169 is 13, by squaring 132 we get 169. 

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, the use of the long division method is easy to find the square root.  The number 169 is a perfect square number because it ends with 9 and when we find the square root of the number we get a whole integer and not the ones with decimals.

Method to find the square root of 169

  • 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
    • 169 = 13 × 13
  • Step 2: Square the common factors
    • 169 = (√13*13)2
    • 169 = 132

There is no step 3 because there is only one common factor square
Hence, √169 = 13

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. 169 – 1 = 168
  2. 168 – 3 = 165
  3. 165 – 5 = 160
  4. 160 – 7 = 153
  5. 153 – 9 = 144
  6. 144 – 11 = 133
  7. 133 – 13 = 120
  8. 120 – 15 = 105
  9. 105 – 17 = 88
  10. 88 – 19 = 69
  11. 69 – 21 = 48
  12. 48 – 23 = 25
  13. 25 – 25 = 0

The step in which we get zero is 13. Hence, √169 = 13

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. 

Hence, √169 = 13

Solved examples

Example 1: The roots of  (169) and -(169) are the same says jack, what did you think?
The negative square has no real root.
169 has real roots while  – (169) has only imaginary roots.

Hence, they are not similar

Example 2: Riya wants to simply 169 to its simplest form, come let’s help her
169 = 13 × 13
Hence the simplest form of  √169 = 13

Example 3: solve 4169 + 3169 
The √169 = 13
= 4 (13) + 3 (13)
= 52 + 39
= 91

Example 4: what is the value of x, if x169 = 13
x169 = 13
169 = 13
Hence, x*13 = 13
X = 13/13 = 1

Therefore x = 1.

Example 5: Find the perimeter of the square if the area of the square tile is 169.
The area of the tile = area = 169 = 13
The square tile has 4 sides therefore we multiply it with 4 = 4*13= 52

Therefore the perimeter of the tile  = 52 units.

Frequently asked questions

What is the square root of 169?
The 169 = 13.

Is 169 a rational number?
Yes, 169 is a rational number because when we divide the number we get 13 and not 0 (p/q≠ 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. 169 = 13 hence 169 is a perfect square number. 

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

Manu bought 169 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.
169 = 13
Therefore, Manu planted 13 plants in each row and column.

What is the square root of 169?
The square root of 169 = 13.

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

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Prerit Jain

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