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Last updated on May 26th, 2025

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Square Root of 289

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The square root of 289 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 289. The number 289 has a unique non-negative square root, called the principal square root.

Square Root of 289 for Qatari Students
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What Is the Square Root of 289?

The square root of 289 is ±17, where 17 is the positive solution of the equation x2 = 289. Finding the square root is just the inverse of squaring a number and hence, squaring 17 will result in 289. The square root of 289 is written as √289 in radical form, where the ‘√’  sign is called  the “radical” sign. In exponential form, it is written as (289)1/2 
 

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Finding the Square Root of 289

We can find the square root of 289 through various methods. They are:

 

  • Prime factorization method

 

  • Long division method

 

  • Repeated subtraction method
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Square Root of 289 By Prime Factorization Method

The prime factorization of 289 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore, i.e., we first prime factorize 289 and then make pairs of two to get the square root.

 

So, Prime factorization of 289 = 17 ×17


Square root of 289= √[17 × 17] = 17

 

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Square Root of 289 By Long Division Method

This method is used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.


Follow the steps to calculate the square root of 289:


 Step 1: Write the number 289 and draw a bar above the pair of digits from right to left.


Step 2: Now, find the greatest number whose square is less than or equal to 2. Here, it is1 because 12=1 < 2


Step 3: now divide 289 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder.  Double the divisor 1, we get 2, and then the largest possible number A1=7 is chosen such that when 7 is written beside the new divisor 2, a 2-digit number is formed →27, and multiplying 7 with 27 gives 189, which
when subtracted from 189, gives 0

Repeat this process until you reach the remainder of 0. 


 
Step 4: The quotient obtained is the square root of 289. In this case, it is 17.

 

 

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Square Root of 289 By Subtraction Method

We know that the sum of the first n odd numbers is n2. We will use this fact to find square roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:


Step 1: take the number 289 and then subtract the first odd number from it. Here, in this case, it is 289-1=288


Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 288, and again subtract the next odd number after 1, which is 3, → 288-3=285. Like this, we have to proceed further.


Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case, it takes 17 steps.


So, the square root is equal to the count, i.e., the square root of 289 is ±17.

 

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Common Mistakes and How to Avoid Them in the Square Root of 289

When we find the square root of 289, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.
 

Mistake 1

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Incorrectly applying the square root property
 

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Square root do not distribute over additions. For example, √289 ≠   √225+√64
 

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Square Root of 289 Examples

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Problem 1

Find √(289⤬256) ?

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√(289⤬256)

 

= 17 ⤬16

 

= 272


Answer : 272
 

Explanation

firstly, we found the values of the square roots of 289 and 256, then multiplied the values.
 

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Problem 2

What is √289 multiplied by 17 ?

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√289 ⤬ 17

 

= 17⤬17

 

= 289


Answer: 289 
 

Explanation

finding the value of √289 and multiplying by 17.
 

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Problem 3

Find the radius of a circle whose area is 289π cm².

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Given, the area of the circle = 289π cm2


Now, area = πr2 (r is the radius of the circle)


So, πr2 = 289π cm2


We get, r2 = 289 cm2


r = √289 cm


Putting the value of √289 in the above equation, 


We get, r = ±17 cm


Here we will consider the positive value of 17.


Therefore, the radius of the circle is 17 cm.


Answer:    17 cm
 

Explanation

We know that, area of a circle = πr2 (r is the radius of the circle).According to this equation, we are getting the value of “r” as 17 cm by finding the value of the square root of 289
 

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Problem 4

Find the length of a side of a square whose area is 289 cm²

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Given, the area = 289 cm2

We know that, (side of a square)2 = area of square

Or,  (side of a square)2 = 289


Or,  (side of a square)= √289


Or, the side of a square = ± 17.


But, the length of a square is a positive quantity only, so, the length of the side is 17 cm.


Answer: 17 cm

Explanation

We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its Square root is the measure of the side of the square
 

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Problem 5

Find √289 / √49

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√289/√49

 

= 17/7  

 

= 2.429


Answer : 2.429 
 

Explanation

we firstly found out the values of √289 and √49, then divided  .

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FAQs on Square Root of 289

1.Is 289 a perfect cube?

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2.Is 17 a factor of 289 ?

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3.Is 289 a perfect square or non-perfect square?

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4.Is the square root of 289 a rational or irrational number?

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5.Is 289 a prime number?

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6.How does learning Algebra help students in Qatar make better decisions in daily life?

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7.How can cultural or local activities in Qatar support learning Algebra topics such as Square Root of 289?

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8.How do technology and digital tools in Qatar support learning Algebra and Square Root of 289?

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9.Does learning Algebra support future career opportunities for students in Qatar?

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Important Glossaries for Square Root of 289

  • Exponential form:An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 ⤬ 2 ⤬ 2 ⤬ 2 = 16 or, 24 = 16, where 2 is the base, 4 is the exponent 

 

  • Factorization: Expressing the given expression as a product of its factors Ex: 48=2 ⤬ 2 ⤬ 2 ⤬ 2 ⤬ 3

 

  • Prime Numbers :Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

 

  • Rational numbers and Irrational numbers:The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

 

  • perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24         
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About BrightChamps in Qatar

At BrightChamps, we know algebra is more than just symbols—it opens doors to many possibilities! Our aim is to support children all over Qatar in mastering key math skills, focusing today on the Square Root of 289 with a special focus on square roots—in a lively, engaging, and easy-to-understand way. Whether your child is calculating the speed of a roller coaster at Qatar’s Angry Birds World, tracking scores at local football matches, or managing their allowance for the latest gadgets, mastering algebra builds their confidence to face everyday challenges. Our interactive lessons make learning both fun and simple. Since kids in Qatar learn in various ways, we tailor our approach to each learner. From Doha’s modern cityscape to desert landscapes, BrightChamps makes math relatable and exciting throughout Qatar. Let’s make square roots a fun part of every child’s math journey!
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Jaskaran Singh Saluja

About the Author

Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.

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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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