Square Root of 16

In Mathematics, the square root of 16 is defined as a number, which on multiplication by itself for two times, results in the original number 16. The value of the square root of 16 is a rational number since it can be represented in the form of p/q. In this article, we will learn two different methods such as the long division method and the prime factorization method to determine the square root of 16 with complete explanation.

Table of Contents:

• What is the Value of Square Root of 16?
• Radical Form of Square Root of 16
• Prime Factorization Method to Find √16
• Long Division Method to Find √16
• Examples
• FAQs

What is the Value of Square Root of 16?

If a number is multiplied by itself and gives the result as 16, then we can say that the number is the square root 16. Symbolically, the square root of 16 is expressed as √16.

Hence, √16 = √(Number × Number)

Hence, by multiplying the number 4 for two times, we get the original number 16.

(i.e) √16 = √(4× 4)

√16 = √(4)²

On removing square and square root, we will get

√16 = ± 4

Square Root of 16 in Radical Form

The simplest radical form of the square root of 16 is √16. Generally, the radical form of the square root of a number can be written, if we know the prime factorization of a number. Thus, the prime factorization of 16 is 2×2×2×2. Thus, if we write the square root of 16 in radical form, it should not be the simplest radical form.

Square Root of 16 by Prime Factorization Method

The square root of 16 can be found using the prime factorization method. To find the value, we should know the prime factorization of 16. Thus, the prime factorization of a number 16 is 2×2×2×2.

Thus, √16 = √(2×2×2×2)

√16 = (√2)². (√2)²

√16 = 2×2 = 4

Hence, the square root of 16 is equal to 4.

Square Root of 16 by Long Division Method

The steps to obtain the square root of 16 using the long division method is provided as follows:

Step 1: First, write the number 16. Next, Pair the number 16 by putting the bar on the top of the number from right to left.

Step 2: Next, divide a number 16 by a number, such that the multiplication of the same number must be less than or equal to 16. Hence, 4×4=16, which is equal to 16.

Step 3: Thus, we get quotient = 4 and remainder = 0.

Step 4: Therefore, the value of the square root of 16, √16 is 4.

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Examples

Example 1:

Simplify the expression: (7√16) + 15.

Solution:

Given: (7√16) + 15.

As we know that the square root of 16 is 4.

Substituting the value in the expression,

(7√16) + 15 = 7(4) + 15

(7√16) + 15 = 28 + 15 =

Therefore, the simplification of (7√16) + 15 is 43.

Example 2:

Determine the value of m, if m+√16 = 20.

Solution:

Given: m+√16 = 20…(1)

We know that √16 = 4

Now, substitute the value in equation (1), we get

m +4 = 20

m = 20-4 = 16

Therefore, the value of m is 16.

Example 3:

Simplify the expression: (5√16 ÷ √16) + 20

Solution:

Given expression: (5√16 ÷ √16) + 20

(5√16 ÷ √16) + 20 = [5(4) ÷ 4] + 20

(5√16 ÷ √16) + 20 = (20/4) + 20

(5√16 ÷ √16) + 20 = 5+ 20

(5√16 ÷ √16) + 20 = 25

Hence, the simplification of (5√16 ÷ √16) + 20 is 25.