Square Root of 16

The square root of 16 is 4. The square root of a number is the inverse of squaring that number, i.e., it gives the original number when multiplied by itself. For example, the square root of 16 is 4 because 4² = 16. In this article, we will learn in detail about the square root of 16.

What is the Square Root of 16?

4 is the square root of 16. Even, It is a number with a square of 16 because the square root of 16 is equal to both 4 and –4, we can obtain 16 by squaring both positive and negative 4. Hence the square root of 16 can be written as ;

√16 = 4
(16)^1/2 = 4

Square Root of 16 Calculator

How to Calculate a Square Root of 16?

A square Root of 16 can be calculated using the following methods:

Prime Factorisation Method
Repeated Subtraction Method
Long Division Method

Square Root of 16 by Prime Factorization Method

Let’s see the following steps of the square root of 16 by using the prime factorization method:

Step 1: The prime factorization of 16 is 16 = 2 × 2 × 2 × 2, 16 = 2^4
Step 2: Now, group the prime factors obtained for 16 in pairs as (2 × 2) × (2 × 2)
Step3: Pick one factor from each pair that can be written in the form: √(2 × 2)² = 4
Step 4: After combining the factor,√16 = 4

Therefore, the square root of 16 is 4.

Read More about Prime Factorization.

Square Root of 16 by Repeated Subtraction Method

In this method, Let’s start with an odd number 1. After that, take the outcome and begin subtracting using the subsequent odd number. Do it until you get the zero.

16-1 = 15
15 – 3 = 12
12 – 5 = 7
7 – 7 = 0

The step in which zero is obtained is 4, Therefore √16 = 4.

Square Root of 16 by Long Division Method

The following procedures must be followed in order to determine the square root of 16:

Step 1: Starting from the right end, begin grouping the numbers into pairs. In the case of 16, both numbers will be combined into a single bar.
Step 2: Now, determine the greatest number 4 that, when multiplied by itself, yields 16 or the smallest number that is most similar to 16.
Step 3: After that, Divide the dividend 16 by 4. Here, 4 is the divisor.
Step 4: Therefore, the square root of 16 is 4.

Is Square Root of 16 Rational or Irrational?

A rational number is any number that can be stated in p/q form, where q = 0, which is the division of two integers. In this case, the square root of 16 is either 4 or (-4) and both the numbers can be represented in the form of a rational number only which can be 4/1 and -(4/1) respectively. So, the square root of 16 is a rational number.

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