289 is a perfect square number i beg your pardon is derived by square the 17. Hence, the square source of 289 is a rational number. In this mini-lesson we will learn to discover square source of 289 along with resolved examples. Let us see what the square root of 289 is.

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Square root of 289289 = 17Square that 289: 2892 = 83,521
1.What Is the Square source of 289?
2.Is Square source of 289 rational or Irrational?
3.How to uncover the Square root of 289?
4.FAQs top top Square source of 289

The initial number who square is 289 gives the square root of 289.

289 = 17

The answer which we obtain on squaring 17 is 289. This renders 289 a perfect square.

A reasonable number can be either terminating or non-terminating and also has a repeating pattern in its decimal part. We witnessed that 289 = 17. 17 is a entirety number. It is possible to express it in p/q form easily. Hence, 289 is a rational number.

There room different methods to uncover the square source of any kind of number. Click here to know more about it.The factors of 289 are, 1, 17 and also 289.As 289 has more than 2 factors, it is a composite number

To discover the square root of 289:

We have the right to use prime factorization method to obtain one number from each pair the the exact same numbers and multiply them. The administer of 289 is 17 × 17 which is composed of 1 pair of the very same number, 17. Thus, the square source of 289 is √(17 × 17) = 17 itself.


Since 289 is a perfect square, we can additionally express it as 172. The number in ~ square source which gets recurring is 17. Hence, the square source of 289 is 17.


The square source of 289 is 17.

Explore Square roots making use of illustrations and interactive examples

Important Notes:

289 is a perfect square together the answer obtained after square source is a rational number.The square source of 289 can be streamlined to 17 either by making use of the prime factorization that 289 or by express 289 as a square the 17.

Think Tank:

Can the value of a square root of 289 it is in decimal?Is -289 a real number? 

Example 1: What is the difference in lengths of square boxes having area 289 square inches and 169 square inches ?


As the area of square crate is area = size × lengthThe length of square box having area 289 square inches is √289 = 17 inches. Similarly the size of box having area 169 square customs is √169 = 13 inches.The distinction in lengths of crate is (17 - 13) inches = 4 inchesHence, the difference in length of square boxes having actually area 289 square inches and 169 square customs is 4 inches.

Example 2: have the right to you determine the radius of circle having area 289π square inches?


Radius deserve to be found using the formula that area of a circle is πr2 square inches. By the provided information,πr2 = 289π r2 = 289By taking the square root on both sides we get, √r2= 289. We recognize that the square root of r2 is r.

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By calculating the square source of 289 is 17 inches.