413 LearnersLast updated on May 26th, 2025
Square root of 16
The square root of 16 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 16. The number 16 has a unique non-negative square root, called the principal square root.
What Is the Square Root of 16?
The square root of 16 is ±4. Finding the square root is just the inverse of squaring a number and hence, squaring 4 will result in 16. The square root of 16 is written as √16 in radical form. In exponential form, it is written as (16)1/2
Finding the Square Root of 16
We can find the square root of 16 through various methods. They are:
- Prime factorization method
- Long division method
- Repeated subtraction method
Square Root of 16 By Prime Factorization Method
The prime factorization of 16 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be separated anymore.
- Find the prime factors of 16
- After factorizing 16, make pairs out of the factors to get the square root.
So, Prime factorization of 16 = 2 × 2 ×2 × 2
Square root of 16 = √[2 × 2 ×2 × 2] = 2 × 2= 4
Square Root of 16 By Long Division Method
This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.
Follow the steps to calculate the square root of 16:
Step 1: Write the number 16 and draw a bar above the pair of digits from right to left.
16 is a 2-digit number, so it is already a pair.
Step 2: Now, find the greatest number whose square is less than or equal to 16. Here, it is 4
Because 42=16
Step 3: Now divide 16 by 4 (the number we got from step 2) and we get a remainder 0.
Step 4: The quotient obtained is the square root. In this case, it is 4.
Square Root of 16 By Subtraction Method
We know that the sum of first n odd numbers is n2. We will use this fact to find square roots through repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:
Step 1: Take the number 16 and then subtract the first odd number from it. Here, in this case, it is 16-1=15
Step 2: We have to subtract the next odd number from the obtained number until it comes zero as a result. Now
take the obtained number (from step 1), i.e., 15 and again subtract the next odd number after 1, which is 3,
15–3=12. Like this, we have to proceed further.
Step 3: Now we have to count the number of subtraction steps it takes to yield 0 finally. Here, in this case it takes 4 steps. So, the square root is equal to the count, i.e., the square root of 16 is ±4.
Common Mistakes and How to Avoid Them in the Square Root of 16
When we find the square root of 16, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions.
Mistake 1
Misunderstanding symbol
Often when √16 is mistaken as 162 , we square the number 16 and get the result of 256. So, understanding of symbols should be clear.
Mistake 2
Ignoring negative root
Remember that both +4 and -4 are valid square roots of 16 where the principal square root is 4, but -4 is also correct.
Mistake 3
Misinterpreting the square root symbol
√16 refers to the positive principal square root. ±√16 will yield both +4 and -4
Mistake 4
Applying square root to non-perfect squares
you have to confirm that 16 is a perfect square before expecting the root will be an integer.
Mistake 5
Confusing square root with division.
Thinking √16 = 16/2 =8, is not the correct concept. Square root concept is not the same as division by 2. It is √16 = ±4
Square root of 16 Examples
Problem 1
Find the radius of a circle whose area is 16π² cm².
Given, the area of the circle = 16π2 cm²
Now, area = πr2 (r is the radius of the circle)
So, πr2 = 16π2 cm2
We get, r2 = 16 cm2
r = √16 cm
Putting the value of √16 in the above equation,
We get, r = ±4 cm
Here we will consider the positive value of 4.
Therefore, the radius of the circle is 4 cm.
Answer: 4 cm.
Explanation
We know that, area of a circle = πr2 (r is the radius of the circle). According to this equation, we are getting the value of “r” as 4 cm by finding the value of the square root of 16.
Problem 2
Find the length of a side of a square whose area is 16 cm².
Given, the area = 16 cm2
We know that, (side of a square)2 = area of square
Or, (side of a square)2 = 16
Or, (side of a square)= √16
Or, side of a square = ± 4.
But, length of a square is a positive quantity only, so, length of the side is 4 cm.
Answer: 4 cm
Explanation
We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily
find out its square root because its Square root is the measure of the side of the square.
Problem 3
Simplify the expression : √16 × √16, √16+√16
√16 × √16
= √(4 × 4) × √(4 × 4)
= 4 × 4
= 16
√16+√16
= √(4 × 4) + √(4 × 4)
= 4 + 4
= 8
Answer: 16, 8
Explanation
In the first expression, we multiplied the value of the square root of 16 with itself.
In the second expression, we added the value of the square root of 16 with itself.
Problem 4
If y=√16, find y²
firstly, y=√16= 4
Now, squaring y, we get,
y2=42=16
or, y2=16
Answer : 16
Explanation
squaring “y” which is same as squaring the value of √16 resulted to 16.
Problem 5
Calculate (√16/4 + √16/2)
Solution :
√16/4 + √16/2
= 4/4 + 4/2
= 1 + 2
= 3
Answer: 3
Explanation
From the given expression, we first found the value of square root of 16 then solved by simple divisions and then simple addition.
FAQs on Square Root of 16
1.Is 16 a perfect square or non-perfect square?
2.Is the square root of 16 a rational or irrational number?
3.What is the principal square root of 16?
4.How is the square root of 16 used in real life?
5.How does the square root of 16 compare to the square root of other numbers?
6.How to solve √17?
Important Glossaries for Square Root of 16
Exponential form:An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 ⤬ 2 ⤬ 2 ⤬ 2 = 16
Or, 24 = 16, where 2 is the base, 4 is the exponent.
Prime Factorization: Expressing the given expression as a product of its factors.
Ex: 48=2 ⤬ 2 ⤬ 2 ⤬ 2 ⤬ 3
Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....
Rational numbers and Irrational numbers - The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.
Perfect and non-perfect square numbers:Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24
Explore More algebra
Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
