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Square Root of 16 + Solution With Free Steps

The square root of any number like 16 is written as √16. The result of this √16 is 4. The resultant 4 is always less than the number for which we take the square root. The number 16 is a perfect square.

In this article, we will analyze and find the square root of 16 using various mathematical techniques, such as the approximation method and the long division method.

What Is the Square Root Of 16?

The square root of the number 16 is 4.

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:

√16 = √(4 x 4)

√16 = √(4)$^2$

√16 = ±4

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining y. Hence 4 is 16’s square root. The square root generates both positive and negative integers.

How To Calculate the Square Root of 16?

You can calculate the square root of 16 using any of two vastly used techniques in mathematics; one is the Approximation technique, and the other is the Long Division method.

The symbol √ is interpreted as 16 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 has 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 16 using the long division method:

Step 1

First, write the given number 16 in the division symbol, as shown in figure 1.

Step 2

Starting from the right side of the number as 16  is two digit number starting with 1 and ending with 6, so divide the complete number 16 directly by considering 16 as pair. 

Step 3

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

Step 4

The resulting quotient 4 is the square root of 16. Figure 1 given below shows the long division process in detail:

Square root of 16 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 detailed steps must be followed to find the square root of 16 using the approximation technique.

Step 1

Consider a perfect square number 4 less than 16.

Step 2

Now divide 16 by 4.

16 ÷ 4 = 4

Step 3

Now take the average of 4 and 4. The resulting number is approximately equivalent to the square root of 16.

(4 + 4) ÷ 2 = 4

Important points

  • The number 16 is a perfect square.
  • The number 16 is rational.
  • The number 16 can be split into its prime factorization.

Is Square Root of 16 a Perfect Square?

The number 16 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 16 is concerned, it is a perfect square. It can be proved as below:

Factorization of 16 results in 4 x 4, which can also be expressed as 4$^2$.

Taking the square root of the above expression gives:

= √(4$^2$)

= (4$^2$)$^{1/2}$

= 4

This shows that 16 is a perfect square and a rational number.

Therefore the above discussion proves that the square root of 16 is equivalent to 4.

Images/mathematical drawings are created with GeoGebra.

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