Last updated on May 26th, 2025
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.
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
We can find the square root of 16 through various methods. They are:
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.
So, Prime factorization of 16 = 2 × 2 ×2 × 2
Square root of 16 = √[2 × 2 ×2 × 2] = 2 × 2= 4
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.
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.
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.
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.
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.
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
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.
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
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.
If y=√16, find y²
firstly, y=√16= 4
Now, squaring y, we get,
y2=42=16
or, y2=16
Answer : 16
squaring “y” which is same as squaring the value of √16 resulted to 16.
Calculate (√16/4 + √16/2)
Solution :
√16/4 + √16/2
= 4/4 + 4/2
= 1 + 2
= 3
Answer: 3
From the given expression, we first found the value of square root of 16 then solved by simple divisions and then simple addition.
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
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.
: He loves to play the quiz with kids through algebra to make kids love it.