Square Root of 1369
A perfect square number is defined as the number which can be found after squaring a whole number. Hence, it can also be defined as the number whose square root always results in a whole number. 1369 is one such number which is obtained after squaring 37. Thus, the square root of 1369 results in a whole number (37). This makes 1369 a perfect square number. Hence, the square root of 1369 is a rational number. In this minilesson, we will learn to find square root of 1369 along with solved examples. Let us see what the square root of 1369 is.
 Square Root of 1369: √1369 = 37
 Square of 1369: 1369^{2} = 18,74,161
What Is the Square Root of 1369?
The number whose square gives 1369 is 37. Thus, the square root of 1369 is 37. It is written as
√1369 = 37
Hence, 1369 is a perfect square number.
Is the Square Root of 1369 Rational or Irrational?
As square root of 1369 is written as √1369 = 37, we can express √1369 in p/q form easily. This makes √1369 a rational number.
How to Find the Square Root of 1369?
We can use different methods to determine the square root of 1369. Click here to know more about it. We will use the two methods given below:
 Square Root of 1369 by Long Division
 Square Root of 1369 by Prime Factorization
Square Root of 1369 by Long Division
The square root of 1369 can be found using the long division as follows.
 Step 1: We pair digits of a given number starting with a digit at one's place. Put a horizontal bar to indicate pairing.
 Step 2: Now we find a number which on multiplication with itself gives a product less than or equal to 13. As we know, 3 × 3 = 9 < 13. Hence, the difference obtained is 4 and the quotient is 3.
 Step 3: Now, we have to bring down 69 and multiply the quotient by 2. This give us 3. Hence, 3 is the starting digit of the new divisor.
 Step 4: 7 is now placed at one's place of new divisor because on multiplication of 67 by 7 we get 469. The obtained answer now is 0. Now the new divisor obtained is 74.
 Step 5: Hence, the square root of 1369 is 37.
Square Root of 1369 by Prime Factorization
1369 is a perfect square hence, we can also express it as (37 × 37). The number within square root which gets repeated is 37. Hence, the square root of 1369 is 37 .
The square root of 1369 is 37.
Explore square roots using illustrations and interactive examples
Important Notes:
 The value obtained after taking square root of a perfect number is always a whole number. Hence, √1369 also results in a whole number.
 The square root of 1369 can be simplified to 37 either by expressing 1369 as a square of 37 or by using the prime factorization of 1369.
Think Tank:
 Is it possible that value of a square root of 1368 is decimal?
 Are the values of √1369 and √1369 same?
Square Root of 1369 Solved Examples

Example 1: How will you determine the difference in lengths of square boxes having area 1369 square inches and 1225 square inches?
Solution
As w the area of square box is area = length × length
The length of square box having area 1369 square inches is √1369 = 37 inches.
Similarly, the length of box having area 1225 square inches is √1225 = 35 inches.
The difference in lengths of boxes is (37  35) inches = 2 inchesHence, the difference in length of square boxes having area 1369 square inches and 1225 square inches is 2 inches.

Example 2: Is the radius of circle having 1369π square inches more than 30 inches?
Solution
Radius can be found using the formula of area of a circle is πr^{2} square inches. By the given information,
πr^{2} = 1369π ⇒ r^{2} = 1369
By taking the square root on both sides we get, √r^{2}= √1369 ⇒ r = √1369
By calculating the square root of 1369 is 37 inches. Hence, the radius of circle having area 1369π square inches will have length more than 30 inches.
FAQs on Square Root of 1369
What are the two square roots of 1369?
The square roots of 1369 are 37 and 37.
Is 1369 a perfect square?
Yes, 1369 is a perfect square.
Does 1369 have a square root?
Yes, 1369 has a square root. The square root of 1369 is 37.
Can square root of 1369 simplified?
1369 can be expressed as a product of 37 × 37. The square root of 1369 gives output as 37.
Is the square root of 1369 rational or irrational?
The square root of 1369 is rational.
Is square root of 1369 a real number?
Yes, the square root of 1369 is a real number.
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