 # Square root of 1369

Square root of 1369 is a value that can be multiplied to itself to get the original number. The square root denotes the root of a number that was squared to get the original number. Thus, if x is the root of 1369, then x2 = 1369. So, we can say, a square root is the reverse procedure of squaring a number.

Since, 1369 is a perfect square, therefore, it’s square root will be a whole number. The square root of 1369 is a rational number that can be represented in the form of P/Q, where P is the numerator and Q is the denominator.

The square root of 1369 is represented by √1369, where ‘√’ is the radical symbol and the number 1369 is the radicand, here. To find the square root, we can use the simple prime factorisation method or long division method.

 Square root of 1369 = √1369 = ±37 Or In Exponent Form, (1369)½ = ±37

Also check:

## How to Find the Square root of 1369?

To find the square root of 1369 we can use the following methods:

### Prime Factorisation Method

The prime factorisation method is one of the easy and most important methods. Using this method, we can write the original number into prime factor form. Hence, we can pair the prime factors that can be written as squared terms.

The prime factorisation of 1369 is:

1369 = 37 x 37

If we write in exponential form, then;

1369 = 372

√1369 = √37

√1369 = 37

Hence, the square root of 1369 is 37, which is also an odd rational number.

 Facts: Square root of 1369 is a natural or a whole number 1369 is an odd number and so is it’s square root 1369 is a perfect square 1369 is evenly divisible by its square root value, thus, 37 is the factor of 1369. The roots of 1369 are +37 or -37

### Long Division Method

The long division method is the quickest method to find the square root of 1369. In this method, we pair the digits starting from the right hand side. After pairing is done, we start dividing the numbers by proper divisors.

Let us find out how.

Step 1: Pair the digits and put bars above each pair as shown in the figure

Step 2: Now we need to divide the first pair on the left hand side, with such a number, that can be multiplied by itself to get a value less than or greater than the dividend (i.e.13). So, 3 x 3 = 9 and 9 is less than 13. Hence, we get the remainder equal to 4 after division.

Step 3: Now again take down the next two digits, i.e. 69 and write them next to 4 (previous remainder)

Step 4: Now add 3 to the previous divisor and write down on the left hand side, as shown in the figure.

Step 5: Taking 7 at the unit place of the divisor and multiplying 67 by 7, we get the value 469, which is equal to the dividend and the remainder becomes zero. Therefore, the square root of 1369 is equal to 37.

### Square Roots of Large Numbers

• Square Root of 5776 = 76
• Square root of 7921 = 89
• Square root of 4489 = 67
• Square root of 3136 = 56
• Square root of 2500 = 50
• Square root of 1600 = 40

## Solved Examples

Q.1: What is the value of 10 multiplied by √1369?

Solution: The value of 10 multiplied by √1369 is:

⇒ 10 x √1369

⇒ 10 x 37

⇒ 370

Q.2: If the area of a square field is 1369 m2, what is the value of its length and breadth?

Solution: Given that,

Area of the field = 1369 m2

Area of the square = Side2

The length and breadth of the square field are equal.

Therefore,

Area of the field = Length2

1369 = Length2

Or

Length = √1369 = 37

Hence, the length of the field is 37 meter.

Q.3: If the area of a square is 1369 units, then find the perimeter of the square.

Solution: Given,

Area of the square = 1369 units

Therefore,

Side of the square = √area = √1369 = 37 unit

Therefore, the perimeter of the square is;

Perimeter = 4 x side = 4 x 37 = 148 units.

## Practice Questions

1. √1369 + √1600 + √2500 = ?
2. What is the cube of 13?
3. What is the square of 19?
4. What is the radical form of the square root of 1369?
5. Why is 1369 a perfect square?

## Frequently Asked Questions on Square root of 1369

### What is the square root of 1369?

The square root of 1369 is equal to 37.
√1369 = 37

### Is the square root of 1369 rational or irrational?

The square root of 1369 is a rational number because it can be expressed as a ratio (P/Q), where Q is not equal to 0.
√1369 = 37 = 37/1
Where 37 is the numerator and 1 is the denominator.

### Is 1369 a perfect square?

Yes, 1369 is a perfect square because the square root of 1369 results in a whole number that can be squared again to get the original number.
√1369 = 37
Or 372 = 1369

### What are the factors of 1369?

The factors of 1369 are 1, 37 and 1369.

### What is the value of √1369 + √400?

√1369 = 37 and √400 = 20
Therefore, √1369 + √400 = 37 + 20 = 57