# Square Root of 1600 + Solution With Free Steps

Let us discuss the square root of the four-digit number in this solution we take 1600 and we find the square root of this number and also see whether it is perfect or not. We can write the square root of 1600 as √1600.

In this article, we will analyze and find the square root of 1600 using various mathematical techniques, such as the approximation method and the long division method.

## What Is the Square Root Of 1600?

The square root of the number 1600 is 40.

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:

√1600 = √(40 x 40)

√1600 = √(40)$^2$

√1600 = ±40

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 40. Hence 40 is 1600’s square root. The square root generates both positive and negative integers.

## How To Calculate the Square Root of 1600?

You can calculate the square root of 1600 using techniques in mathematics; like the Long Division method.

The symbol √ is interpreted as 1600 raised to the power 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 1600 using the long division method:

### Step 1

First, write the given number 1600 in the division symbol, as shown in figure 1.

### Step 2

Starting from the right side of the number, divide the number 1600 into pairs such as 00 and 16.

### Step 3

Now divide the digit 16 by a number, giving a number either 16 or less than 16. Therefore, in this case, the remainder is zero, whereas the quotient 4.

### Step 4

After this, bring down the next pair 00. Now the dividend is 00. To find the next divisor, we need to double our quotient obtained before. Doubling 4 gives 8; hence consider it as the next divisor.

### Step 5

Now pair 8 with another number to make a new divisor that results in $\leq$ 00 when multiplied by 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 0 to the divisor and multiplying 80 with 0 results in 0 $\eq$ 0. The remainder obtained is 0.

### Step 7

The resulting quotient 40 is the square root of 1600. Figure 1 given below shows the long division process in detail:

figure 1

### Important points

• The number 1600 is a perfect square.
• The number 1600 is a rational number.
• The number 1600 can be split into its prime factorization.

## Is Square Root of 1600 a Perfect Square?

The number 1600 is 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 1600 is concerned, it is a perfect square. It can be proved as below:

Factorization of 1600 results in 40 x 40 which can also be expressed as 40$^2$.

Taking the square root of the above expression gives:

= √(40$^2$)

= (40$^2$)$^{1/2}$

= 40

This shows that 1600 is a perfect square and a rational number.

Therefore the above discussion proves that the square root of 1600 is equivalent to 40.

Images/mathematical drawings are created with GeoGebra.