Square Root of 320

The square root of a number is the value when multiplied by itself gives the original number. For example, 13 × 13 = 169, so the square root of 169 is 13. In this mini-lesson, we will learn about the square root of 320. We will do so using methods like prime factorization and long division method. The square root of 320 is a number which when multiplied by itself, results in the number 320. 320 is an even number and a composite number. Let us determine the square root of 320 in this article. We will learn how to calculate the square root of 320, is square root of 320 a rational or irrational, and look at a few problems to help us understand this topic.

• Square Root of 320: √320 = 17.888
• Square of 320: 320^² = 102,400

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 320 can be written as:

• Radical form: √320 
• Decimal form: 17.888    
• Exponent form: (320)^½

320 cannot be broken into two equal number (y) which on multiplying together (y × y) give 320. It can be approximately written as a square of 17.888, 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 320 is an irrational number.

• 320 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
• Square root of 320 is simlified in decimal form as √320 = 17.888
• Square root of 320 cannot be expressed as a fraction in the form p/q which tells us that the square root of 320 is an irrational number.

There are 2 ways to find the square root of 320:

• Long Division Method
• Prime Factorization

Long Division Method

The square root of 320 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 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., 20.
• The double of 1 is 2. Now a number is to be placed along with 2, i.e., 7. The product of 27 by 7 gives 189. When the difference between 220 and 189 is taken, the remainder is 31.
• 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 34 is added in the blank and it is multiplied by the same number in the quotient. Product of 348 with 8 gives 2784.
• The difference obtained from the above step is 3100 - 2784 = 316.
• The process is repeated the same way. 

Therefore, the square root of 320 = 17.88

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

• What is the negative root of 3200?
• Find the square root of 320 up to 5 decimal places?
• What is the square root of:
  a) 32030
  b) 3205320

What is the square root of 320 using prime factorization?

Prime factorization of 320 = 2⁶ × 5
Simplified form of √320 is = 8√5
Square root of 5  is 2.23606.
√320 = 8 × 2.23606 = 17.888
Therefore, the square root of √320 = 15.62048

Is 320 a perfect square root?

320 is not a perfect square. 320 is a natural number, but since there is no other natural number that can be squared to result in the number 320, it is NOT a perfect square.

What is the decimal value of the square root of 320?

The decimal value of the square root of 320 is √320 = 17.888.

Is the square root of 320 a rational number?

No, the square root of 320 is not a rational number since the square root of 320 is non-terminating and cannot be represented in the form of p/q.

Can we find the square root of 320 by the repeated subtraction method?

No, we can’t find the square root of 320 by repeated subtraction method as it can be used only for perfect squares. 320 is not a perfect square.