Table Of Contents

136 Learners

Last updated on ** September 24th, 2024**

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:

- Prime factorization method

- Long division method

- Repeated subtraction 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

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 4^{2}=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.

**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, 2^{4} = 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