Square Root Of 320 Simplified

Foursquare Root of 320

The foursquare root of a number is the value when multiplied by itself gives the original number. For instance, 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 and so using methods similar 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 u.s. decide the foursquare root of 320 in this article. We will acquire how to summate 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

What Is the Square Root of 320?

The foursquare root of a number north is written every bit √north. This number when squared or multiplied past itself results in the original number n. The foursquare root of 320 tin can exist written as:

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

Is Foursquare Root of 320 Rational or Irrational?

320 cannot be broken into two equal number (y) which on multiplying together (y × y) requite 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 non have a natural number every bit its foursquare root.
Square root of 320 is simlified in decimal course as √320 = 17.888
Square root of 320 cannot be expressed as a fraction in the form p/q which tells the states that the square root of 320 is an irrational number.

How to Find the Foursquare Root of 320?

At that place are ii means to find the square root of 320:

Long Division Method
Prime Factorization

Long Partition 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 equally shown in image.
The first pair only consists of 1 number, i.due east., 3. Square of 1 gives a product less than three. The number is subtracted from the first pair and afterward, the next pair is added every bit the divisor, i.e., xx.
The double of 1 is ii. Now a number is to be placed forth with 2, i.eastward., 7. The product of 27 by 7 gives 189. When the difference betwixt 220 and 189 is taken, the residual is 31.
Now double of the quotient is taken. Now a decimal is added to the caliber, hence letting us add together a pair of zeros to the original dividend. A number along with 34 is added in the blank and it is multiplied by the aforementioned number in the quotient. Product of 348 with viii gives 2784.
The departure obtained from the above step is 3100 - 2784 = 316.
The procedure is repeated the aforementioned way.

Square root of 320

Therefore, the square root of 320 = 17.88

Explore square roots using illustrations and interactive examples

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Challenging Questions

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

Example i: The area of square shaped plot is 320 square units. Calculate the measurement of 1 side of a land.

Solution:

The area of land = 320 sq. units
To find the side of a square-shaped tabular array, allow u.s. take square root of 320 by prime number factorization method.
320 = 2⁶ × 5
√320 = 8√5
Foursquare root of 320 is 17.888.
Therefore, side of square plot is 17.888 units.
Example ii: Tim is multiplying a number by itself. If the production is 320, help Tim in finding the number.

Solution:

To find the number allow us assume number = a
On multiplying a times a = a × a = 320
a² = 320
a = √320
a = 17.888
(17.888 × 17.888 = 319.980 ≅ 320)
The number is 17.888.

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FAQs on Square Root of 320

What is the square root of 320 using prime factorization?

Prime factorization of 320 = ii⁶ × 5
Simplified form of √320 is = 8√5
Foursquare root of v is 2.23606.
√320 = 8 × ii.23606 = 17.888
Therefore, the square root of √320 = 15.62048

Is 320 a perfect square root?

320 is not a perfect foursquare. 320 is a natural number, just since at that place is no other natural number that tin can exist 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 foursquare 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 observe the square root of 320 by repeated subtraction method as it can be used merely for perfect squares. 320 is not a perfect foursquare.