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# Square Root of 300 + Solution With Free Steps

300 has a square root of 17.32. The long division approach and an approximation method will both be used in this article to determine the square root of 300. The integer whose square root is to be determined is always greater than the square root. The square root of 300 is not a perfect one.

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In this article, we will analyze and find the **square root of 300**Â using various mathematical techniques, such as the approximation method and the long division method.

## What Is the Square Root Of 300?

**The square root of the number 300 is 17.32.**

The** square root** can be defined as the quantity that can be doubled to produce the square of that similar quantity. In simple words, it can be explained as:

**âˆš300 = âˆš(17.32 x 17.32)**

**âˆš300 = âˆš(17.32)$^2$**

**âˆš300 = Â±17.32**

The square can be canceled with the square root as it is **equivalent to 1/2**; therefore, obtaining 17.32. Hence 17.32 is 300’s square root. The square root generates both **positive** and **negative integers**.

## How To Calculate the Square Root of 300?

You can calculate the **square root of 300**Â using any of two vastly used techniques in mathematics; one is the **Approximation technique**, and the other is the **Long Division method**.

The symbolÂ **âˆšÂ **is interpreted asÂ **300**Â raised to the power**Â 1/2**. So any number, when multiplied by itself, produces its square, and when the square root of any squared number is taken, it produces the actual number.

Let us discuss each of them to understand the concepts better.

### Square Root by Long Division Method

The process of **long division **is one of the most common methods used to find the square roots of a given number. It is easy to comprehend and provides more reliable and accurate answers. The long division method reduces a multi-digit number to its equal parts.

Learning how to find the **square root** of a number is easy with the long division method. All you need are five primary operations- divide, multiply, subtract, bring down or raise, then repeat.

Following are the simple steps that must be followed to find the square root of 300Â using the long division method:

### Step 1

First, write the given **number 300**Â in the division symbol, as shown in figure 1.

### Step 2

Starting from the right side of the number, divide the number 300 into **pairs** such as 00 and 3.

### Step 3

Now divide the digit 3 by a number, giving a number either 1 or less than 1. Therefore, in this case, the remainder is 2 whereas the quotient is one.

### Step 4

After this, bring down the next pair 00. Now the **dividend** is 200. To find the next divisor, we need to double our quotient obtained before. Doubling 1 gives 2; hence consider it as the next divisor.

### Step 5

Now pair 2 with another number to make a new divisor that results in $\leq$ 200 when multiplied with the divisor. If the number is **not a perfect square**, add pair of zeros to the right of the number before starting division.

### Step 6

Adding 7 to the divisor and multiplying 27 with p results in 189 **<** 200. The remainder obtained is 11. Move the next pair of zeros down and repeat the same process mentioned above.

### Step 7

Keep on repeating the same steps till the zero remainder is obtained or if the division process continues infinitely, solve to two decimal places.

### Step 8

The resulting quotient 17.32 is the square root of 300. Figure 1 given below shows the long division process in detail:

Figure 1

### Square Root by Approximation Method

The **approximation method** involves guessing the square root of the non-perfect square number by dividing it by the perfect square lesser or greater than that number and taking the average.

The given detailed steps must be followed to find the **square root of 300**Â using the approximation technique.

### Step 1

Consider a perfect square number 17 less than 300.

### Step 2

Now divide 300 by 17.

**300 Ã· 17 = 17.64**

### Step 3

Now take the average of 17 and 17.64. The resulting number is approximately equivalent to the square root of 300.

**(17 + 17.64) Ã· 2 = 17.32**

### Important points

- The number 300 is not a perfect square.
- The number 300 is an irrational number.
- The number 300 can be split into its prime factorization.

## Is Square Root of 300 a Perfect Square?

The number 300 is **Â not a perfect square**. A number is a perfect square if it splits into two equal parts or identical whole numbers. If a number is a perfect square, it is also rational.

A number expressed in p/q form is called a **rational number**. All the natural numbers are rational. A square root of a perfect square is a whole number; therefore, a perfect square is a rational number.

A number that is not a perfect square is** irrational** as it is a decimal number. As far as 300 is concerned, it is not a perfect square. It can be proved as below:

Factorization of 300 results in 3 x 300.

Taking the square root of the above expression gives:

**= âˆš(3 x 300)**

**= (3 x 300)$^{1/2}$**

**=17.32**

This shows that 300 is not a perfect square as it has decimal places; hence it is an irrational number.

Therefore the above discussion proves that the square root of 300 is equivalent to 17.32.

*Images/mathematical drawings are created with GeoGebra.*