Square Root of 16

The square root of 16 is expressed as √16 in the radical form and as (16)^½ or (16)^0.5 in the exponent form. The square root of 16 is 4. It is the positive solution of the equation x² = 16. The number 16 is a perfect square.

• Square Root of 16: 4
• Square Root of 16 in exponential form: (16)^½ or (16)^0.5
• Square Root of 16 in radical form: √16

The square root of a number is the number that gets multiplied to itself to give the product. For any two real numbers a and b,

a² = b

a = √b

The above expression means that a is the 2nd root or square root of b. The square root of 16 means that number which when multiplied with itself will give the result as 16. The definition above can be represented as,

Square root of 16 = √16 

4² = 4 × 4 is 16
Here 4 is called the square root of 16
16 is a perfect square.
So the square root of 16 is 4. The square root of 16 is the inverse operation of squaring 4 and -4
4 × 4 = 16
(-4) × (-4) = 16

A rational number is defined as the number that can be expressed in the form of a quotient or division of two integers i.e., p/q, where q = 0. In the above section, we observed diagrammatically that the square root of 16 is either 4 or (-4) Both the numbers can be represented in the form of a rational number i.e., 4/1 and -(4/1) respectively.
√16 = 4 = 4/1
Thus, the square root of 16 is rational.
So √16 is an irrational number.

The square root of 16 can be calculated using different methods: Prime Factorization and Long Division method. Let us see how it is calculated using Prime Factorization:

Square Root of 16 by Prime Factorization

Following steps can be followed using prime factorization:

• Step 1. Determine the prime factorization of 16 
  16 = 2 × 2 × 2 × 2
  16 = 2 × 2
• Step 2. Group the prime factors obtained for 16 in pairs.
• Step 3. Pick one factor from each pair and they can be written in the form: 
• Step 4. Thus, following the law of exponents, we get,

√16 = √ (2 × 2)²

√16 = (4²)^½ = 4

Let us now try finding the square root of 16 by the long division method!

Square Root of 16 By Long Division

Here are the steps that need to be followed to calculate the square root of 16:

• Step 1. Write 16 as shown in the figure. Start grouping the number in pairs from the right end. For 16, both the numbers will be grouped under one bar.  
• Step 2. Find the largest number that when multiplied with itself will give 16 or a smaller number closest to 16. 4 is the required number.
• Step 3. Perform division on the dividend 16, using 4 as the divisor.
• Step 4. The quotient obtained from the long division is the square root of 16

Explore Square roots using illustrations and interactive examples

• Square Root of 64
• Square Root of 36
• Square Root of 169
• Square Root of 25
• Square Root of 81

Think Tank:

• Jenny has a square table that has an area of 16 square inches. She covered it with a table cloth of area 25 square inches. How many inches does the cloth hang over the table on each side if put centered?

Important Notes:

• The square root of 16  is expressed as √16 in the radical form and as 16^1/2 in exponential form.
• The square root of a number is both negative and positive for the same numerical value i.e., the square root of 16 will be 4.