Square Root

# What is the square root of 16? How to find the square root of 16?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What is the square root of 16? How to find the square root of 16?

The square root of 16 is 4. The square root of a number is the inversion of squaring the given numbers or when the value is multiplied by itself it gives the original value. Let us take 16 as an example. The 16 is 4 and by squaring 4^{2 }we get 16.

The square root symbol is denoted as √ before going ahead with any number for finding their square root we have to check whether the given number is a perfect square number or not. The perfect square is the number that when squared has a whole number like √36 = 6. The non-perfect square numbers are the ones that don’t have a square number when they are squared like √10 = 3.162.

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**Rational and irrational numbers**

Rational numbers are the ones that when divided are not equal to zero let us take two values p and q, by dividing p with q, p/q≠ 0. They are usually a whole number.

For an irrational number, the remainder is not a whole number but the one with the decimal. Let us take p and q when they are divided they are not equal to zero and are not expressed as the ratio of two integers.

**How to find the square root of 16?**

The given number 16 is a perfect square, rational number. To find the square root three methods are used.

- Long division method
- Prime factorization method
- Repeated subtraction method

**Long division method**

Choose the number that when multiplied twice the result is 16. The number when multiplied twice gives 16 is 4. Hence 4 is the divisor.

Hence, the √**16 = 4.**

**Prime factorization method**

To find the square root of a number using the prime factorization method. First, find the prime factors of the given number. Let n be the factors when squaring a similar number we get n^{2} by multiplying the remaining square we get the square root of the number.

Prime factor of 16 = 2×2×2×2 or 2^{4}

Now let us take the similar squares

Now, multiply the squares 2×2 = 4

Hence, the √**16 = 4.**

**Repeated subtraction**

Start to subtract the number with odd numbers. The first odd number to go is 1. Then take the result and start subtracting with the next odd number. Repeat the steps until you reach zero. The step in which zero is attained is the square root of the number.

- 16-1 = 15
- 15 – 3 = 12
- 12 – 5 = 7
- 7 – 7 = 0

The step in which zero is obtained is 4, Hence, √**16 = 4.**

**Solved examples**

**Q1: If the area of the circle is 16 square inches, find the circle’s radius.****A1: **Area of the square = πr2

πr2 = 16

Since π is common we will cancel that

We get r^{2} = 16

r= √**16 **

The radius of the circle is 4 inches.

**Q2: Solve 6 √16 ÷2 √16 **

**A2:**The square root of

**16 =**4

= 6 (4)

**÷**2 (4)

= 24

**÷**8

Hence by solving we get 3

**Q 3: A farmer brings 16 saplings if the number of saplings has to be equal in the same row and column how many saplings can be there?****A3:** Total number of saplings = 16

When they need to be planted equally then the number has to be equally split,

By taking the square root 16** **we get 4

Hence, 4 people are seated equally in both row and column.

**Q4: Romie wants to simply 16 to its simplest form, let’s help her**.**A4: **16 = 4 × 4

Hence the simplest form of **16 = 4**

**Q5: what is the value of x, if x √16 = 16**

**A5:**x16 = 16

**√**16 = 4

Hence, x 4 = 16

X = 16

**÷**4 = 4

Therefore x = 4.

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**Frequently asked questions**

**What is the square root of 16?**

The prime factor of 16 = 16 = 4 × 4

The 16 = 4.

**What is a perfect square number?**

A perfect square number is one when we find the root of the number we get a whole number and not a decimal. **√**16 = 4 hence 16 is a perfect square number.

**Is 16 a rational number?**

Yes, 16 is a rational number because when we divide the number we get 4 and not 0 (p/q≠ 0)

**What is the square root of 400?**

The **√**400 = 20

**What is the square root of 225?**

The square root of 225 = 15.

**What are the methods to find the square root of a number?**

There are three methods to find the square root of a number

Prime factorization method

Long division method

Repeated subtraction

**How to find the square root for irrational numbers?**

To find the square root for irrational numbers use the long division method

Written by

Prerit Jain