Square Root

# What Is the Square Root of 225? How to Find the Square Root of 225?

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

### What Is the Square Root of 225? How to Find the Square Root of 225?

The square root of 225 is 15. When the addition is inversed we get subtraction, when multiplication is inversed we get division when we inverse the square root of a number we get by squaring the values. When a value is multiplied by itself we get the original value. Let us take 225 as an example.

When the number 15 is multiplied by itself (15×15) we get 225 and by squaring 15^{2} we get 225. They are denoted as a rational symbol √ and the exponential form is expressed as (15)^{0.5} or (15)^{½} since p/q ≠ 0 and they have a whole number as their quotient they are rational and a perfect square number.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

**Methods to find the square root of 225**

There are three methods to find the square root of the number for the rational and perfect square values.

- Long division method
- Prime factorization method
- Repeated subtraction

**Long division method**

The long division operates by taking the nearest integer when divided gives the number. The division is continued for perfect square numbers until zero is reached.

Hence, √**225 = 15**

**Prime factorization method**

Prime factorization is one of the easiest ways to find the square root of a number.

**Step 1:**Find the prime factors of 225- The prime factors of 225 = 3×3×5×5

**Step 2:**Square the similar factors n2- √225 = 32 × 52

**Step 3:**Multiply the squares- 225 = 3 × 5
- Hence, √225 = 15

**Repeated subtraction method**

Repeated subtraction is carried out by subtracting the number that is odds. The step is continued until zero is obtained.

- 225 – 1 = 224
- 224 – 3 = 221
- 221 – 5 = 216
- 216 – 7 = 209
- 209 – 9 = 200
- 200 – 11= 189
- 189 – 13 = 176
- 176 – 15 = 161
- 161 – 17 = 144
- 144 – 19 = 125
- 125 – 21 = 104
- 104 – 23 = 81
- 81 – 25 = 56
- 56 – 27 = 29
- 29 – 29 = 0

The step in which zero is obtained is the 15th one

Hence, √225** = 15**

**Solved examples**

**Q1: If the area of the circle is 225 π** **square inches find the radius of the circle.**

A1: Area of the square = πr2

πr2 = 225π

Since π is common we will cancel that

We get r^{2} = 225

r= √225** **

The radius of the circle is 15 inches.

**Q2: Solve 2 √225 + 1 √225**

A2: The square root of** **225** = **15

=2 (15) + 1 (15)

= 30+15

=45

**Q3: Class C has 225 students if the number of students to be seated should be equal in the same row and column. how many students can sit in a row?**

A3: The total number of students = 225

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

By taking the square root 225** **we get 15

Hence, 15 people are seated equally in both rows and columns.

**Q4: Stacy wants to simply 225 to its simplest form, let’s help her**.

A4: 225 = 3^{2} ×5^{2}

√225 = 15

**Q5: what is the value of x if x √225 = 60**

A5: x

**√**225 = 60

**√**225 = 15

Hence, x 15 = 60

X = 60/15 = 6.6

Therefore x = 6.6.

Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep.

**Frequently asked questions**

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

225 = 3^{2} ×5^{2}

√225 = 15

The square root of 225 = 15.

**Explain why the square root of 225 is a rational number**

When finding the prime factor of 225 we get 15^{2} which is entirely an even power hence all the numbers are positive integers which makes them rational numbers.

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

The square root of 225 is 15,

therefore 225√225

225 × 15 = 3375

**What is the real value for the square root of 225**

The actual value for the 225 = 15.

When the number 15 is multiplied by itself (15×15) we get 225 and by squaring 15^{2} we get 225.

**What is the square root of 900?**

The prime factor of 900 = 2 × 2 × 3 × 3 × 5 × 5

The square root of 900 = 30

**What is the square root of (-225)?**

The square root of minus digits is imaginary numbers or imaginary units which really don’t have a square root.1

Hence, the √225 = 15i

**Is 225 a perfect square number?**

Yes, 225 is a perfect square number.

When the square root of the number is squared we get the given number.

We hope that this article has helped you in clearing your queries on the square root of 225!

Written by by

Prerit Jain