Square Root of 369

The square root of a number is the value which when multiplied by itself gives the original number. For example, 19 × 19 = 361. So, the square root of 361 is 19. In this mini-lesson, we will learn about the square root of 369. We will do so using methods like long division. The square root of 369 is a number which when multiplied by itself, results in the number 369. 369 is an odd number and a composite number. Let us determine the square root of 369 in this article. We will learn how to calculate the square root of 369, find out if the square root of 369 is rational or irrational, and look at a few problems to help us understand this topic.

• Square Root of 369: √369 = 19.2
• Square of 369: 369^² = 136161

If a number is a perfect square, it is easy to evaluate the square root using the inverse operation of the squaring operation. 369 is not a perfect square. √369 can be evaluated using the long division method. The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 369 can be written as: 

• Radical form: √369 
• Decimal form: 19.2    
• Exponent form: (369)^½

The square root of 369 is a non-repeating and non-terminating number. So, it cannot be expressed in the form of p/q where q ≠ 0. Hence, the square root of 369 is an irrational number. 369 cannot be broken into two equal factors which on multiplying give 369. It can be approximately written as a square of 19.2, which is a non-recurring and non-terminating decimal number. This shows it isn't a perfect square, which also proves that the square root of 369 is an irrational number.

There are 2 ways to find the square root of 369:

• Long Division Method
• Prime Factorization

Long Division Method

The square root of 369 by long division method consists of the following steps:

• Pair the digits of the number from one's digit by placing a bar over them as shown in the image.
• The first pair just consists of 1 number, i.e., 3. Square of 1 gives a product less than 3. The number is subtracted from the first pair and subsequently, the next pair is added as the divisor, i.e., 69.
• The double of 1 is 2. Now a number is to be placed along with 2, i.e., 9. The product of 29 by 9 gives 261. When the difference between 269 and 261 is taken, the remainder is 8.
• Now double of the quotient is taken. Now a decimal is added to the quotient, hence letting us add a pair of zeros to the original dividend. A number along with 38 is added in the blank and it is multiplied by the same number in the quotient. Product of 382 with 2 gives 764.
• The difference obtained from the above step is 800 - 764 = 36.
• The process is repeated the same way. 

Therefore, the square root of 369 = 19.2

The square root of 369 by prime factorization:

Prime factorization of 369 = 3 × 3 × 41
Simplified form of √369 is = 3√41
Square root of 41  is 6.4031.
√369 = 3 × 6.4031 = 19.2
Therefore, the square root of √369 = 19.209

• 369 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
• Square root of 369 is simlified in decimal form as,√369 = 19.2
• Square root of 369 cannot be expressed as a fraction if the form p/q which tells us that the square root of 369 is an irrational number.

Explore square roots using illustrations and interactive examples

• Square Root of 361
• Square Root of 324
• Square Root of 289
• Square Root of 300
• Square Root of 250
• Square Root of 288
• Square Root of 69

• What is the negative root of 3690?
• Find the square root of 369 up to 5 decimal places?
• What is the square root of:
  a) 36996
  b) 369469

What is the square root of 369 using prime factorization?

Prime factorization of 369 = 3 × 3 × 41
Simplified form of √369 is = 3√41
Square root of 41  is 6.4031.
√369 = 3 × 6.4031 = 19.2
Therefore, the square root of √369 = 19.209

Is 369 a perfect square root?

369 is not a perfect square. 369 is a natural number, but since there is no other natural number that can be squared to result in the number 369, it is NOT a perfect square.

What is the decimal value of the square root of 369?

The decimal value of the square root of 369 is √369 = 19.209.

Is the square root of 369 a rational number?

No, the square root of 369 is not a rational number since the square root of 369 is non-terminating and cannot be represented in the form of p/q where q ≠ 0.

Can we find the square root of 369 by the repeated subtraction method?

No, we can’t find the square root of 369 by repeated subtraction method as it can be used only for perfect squares. 369 is not a perfect square.