BrightChamps Logo
Login
Creative Math Ideas Image
Live Math Learners Count Icon102 Learners

Last updated on May 26th, 2025

Math Whiteboard Illustration

Square Root of 213

Professor Greenline Explaining Math Concepts

If a number is multiplied by the same number, the result is a square. The inverse of the square is a square root. The square root is used in fields such as vehicle design and finance. Here, we will discuss the square root of 213.

Square Root of 213 for Indonesian Students
Professor Greenline from BrightChamps

What is the Square Root of 213?

The square root is the inverse of the square of the number. 213 is not a perfect square. The square root of 213 is expressed in both radical and exponential form. In the radical form, it is expressed as √213, whereas (213)^(1/2) in the exponential form. √213 ≈ 14.5945, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

Professor Greenline from BrightChamps

Finding the Square Root of 213

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the long-division method and approximation method are used. Let us now learn the following methods:

 

  • Prime factorization method
     
  • Long division method
     
  • Approximation method
Professor Greenline from BrightChamps

Square Root of 213 by Prime Factorization Method

The product of prime factors is the prime factorization of a number. Now let us look at how 213 is broken down into its prime factors:

 

Step 1: Finding the prime factors of 213 Breaking it down, we get 3 x 71: 3^1 x 71^1

 

Step 2: Now we have found the prime factors of 213. Since 213 is not a perfect square, the digits of the number can’t be grouped in pairs.

 

Therefore, calculating √213 using prime factorization is not feasible.

Professor Greenline from BrightChamps

Square Root of 213 by Long Division Method

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step:

 

Step 1: To begin with, we need to group the numbers from right to left. In the case of 213, we group it as 13 and 2.

 

Step 2: Now we need to find n whose square is less than or equal to 2. We can say n as ‘1’ because 1 x 1 is less than or equal to 2. Now the quotient is 1, and after subtracting 1 from 2, the remainder is 1.

 

Step 3: Bring down 13, which is the new dividend. Add the old divisor with the same number: 1 + 1 = 2, which will be our new divisor.

 

Step 4: The new divisor will be 2n. We need to find the value of n.

 

Step 5: Find 2n × n ≤ 113. Let us consider n as 4, now 24 x 4 = 96.

 

Step 6: Subtract 96 from 113; the difference is 17, and the quotient is 14.

 

Step 7: Since the dividend is less than the divisor, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1700.

 

Step 8: Find the new divisor, let’s say it is 145, because 145 x 5 = 725.

 

Step 9: Subtracting 725 from 1700 gives the result 975.

 

Step 10: Now the quotient is 14.5

 

Step 11: Continue doing these steps until we get two numbers after the decimal point. If there is no decimal value, continue until the remainder is zero.

 

So the square root of √213 is approximately 14.59.

Professor Greenline from BrightChamps

Square Root of 213 by Approximation Method

The approximation method is another method for finding square roots. It is an easy method to find the square root of a given number. Now let us learn how to find the square root of 213 using the approximation method.

 

Step 1: Find the closest perfect squares to √213. The smallest perfect square less than 213 is 196, and the largest perfect square greater than 213 is 225. √213 falls between 14 and 15.

 

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula, (213 - 196) ÷ (225 - 196) = 17 ÷ 29 ≈ 0.5862. Adding the initial integer value to the decimal, 14 + 0.59 = 14.59, so the square root of 213 is approximately 14.59.

Max Pointing Out Common Math Mistakes

Common Mistakes and How to Avoid Them in the Square Root of 213

Students make several mistakes while finding square roots, such as forgetting about the negative square root or skipping steps in the long division method. Let's explore a few common mistakes in detail.

Mistake 1

Red Cross Icon Indicating Mistakes to Avoid in This Math Topic

Forgetting about the negative square root

Green Checkmark Icon Indicating Correct Solutions in This Math Topic

It is important to make students aware that a number has both positive and negative square roots. However, we typically use only the positive square root in most practical applications.

 

For example: √50 ≈ 7.07, but there is also -7.07.

Max from BrightChamps Saying "Hey"

Square Root of 213 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Can you help Max find the area of a square box if its side length is given as √213?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The area of the square is 213 square units.

Explanation

The area of the square = side².

The side length is given as √213.

Area of the square = side² = √213 × √213 = 213.

Therefore, the area of the square box is 213 square units.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 2

A square-shaped building measuring 213 square feet is built; if each of the sides is √213, what will be the square feet of half of the building?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

106.5 square meters.

Explanation

We can just divide the given area by 2 as the building is square-shaped.

Dividing 213 by 2 gives us 106.5.

So half of the building measures 106.5 square meters.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 3

Calculate √213 × 5.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

Approximately 72.97.

Explanation

First, find the square root of 213, which is approximately 14.59.

Then multiply 14.59 by 5. So 14.59 × 5 ≈ 72.97.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 4

What will be the square root of (213 + 12)?

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The square root is 15.

Explanation

To find the square root, first calculate the sum of (213 + 12). 213 + 12 = 225, and then √225 = 15.

Therefore, the square root of (213 + 12) is ±15.

Max from BrightChamps Praising Clear Math Explanations
Max, the Girl Character from BrightChamps

Problem 5

Find the perimeter of the rectangle if its length ‘l’ is √213 units and the width ‘w’ is 30 units.

Ray, the Boy Character from BrightChamps Saying "Let’s Begin"

The perimeter of the rectangle is approximately 89.19 units.

Explanation

Perimeter of the rectangle = 2 × (length + width)

Perimeter = 2 × (√213 + 30) ≈ 2 × (14.59 + 30) ≈ 2 × 44.59 ≈ 89.19 units.

Max from BrightChamps Praising Clear Math Explanations
Ray Thinking Deeply About Math Problems

FAQ on Square Root of 213

1.What is √213 in its simplest form?

Math FAQ Answers Dropdown Arrow

2.Mention the factors of 213.

Math FAQ Answers Dropdown Arrow

3.Calculate the square of 213.

Math FAQ Answers Dropdown Arrow

4.Is 213 a prime number?

Math FAQ Answers Dropdown Arrow

5.213 is divisible by?

Math FAQ Answers Dropdown Arrow

6.How does learning Algebra help students in Indonesia make better decisions in daily life?

Math FAQ Answers Dropdown Arrow

7.How can cultural or local activities in Indonesia support learning Algebra topics such as Square Root of 213?

Math FAQ Answers Dropdown Arrow

8.How do technology and digital tools in Indonesia support learning Algebra and Square Root of 213?

Math FAQ Answers Dropdown Arrow

9.Does learning Algebra support future career opportunities for students in Indonesia?

Math FAQ Answers Dropdown Arrow
Professor Greenline from BrightChamps

Important Glossaries for the Square Root of 213

  • Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, which is √16 = 4.

 

  • Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

 

  • Principal square root: A number has both positive and negative square roots; the positive square root is often used in practical applications. This is known as the principal square root.

 

  • Integer: An integer is a whole number that can be positive, negative, or zero. Examples include -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7.

 

  • Approximation: Approximation is a method used to find a value that is close to the actual value. For example, the square root of 213 is approximately 14.59.
Professor Greenline from BrightChamps

About BrightChamps in Indonesia

At BrightChamps, we believe algebra is more than symbols—it’s a doorway to endless possibilities! We aim to help children throughout Indonesia master key math skills, focusing today on the Square Root of 213 with a special emphasis on square roots—in a way that’s fun, lively, and easy to understand. Whether your child is measuring the speed of a roller coaster at Dunia Fantasi, tracking scores in badminton matches, or managing their allowance for the latest gadgets, mastering algebra builds the confidence they need for everyday problems. Our hands-on lessons make learning simple and enjoyable. Because children in Indonesia learn differently, we tailor our approach to fit each learner’s needs. From Jakarta’s bustling streets to Bali’s scenic beaches, BrightChamps brings math to life, making it relevant and exciting across Indonesia. Let’s make square roots a fun part of every child’s math journey!
Math Teacher Background Image
Math Teacher Image

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.

Math Teacher Fun Facts Image
Max, the Girl Character from BrightChamps

Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

INDONESIA - Axa Tower 45th floor, JL prof. Dr Satrio Kav. 18, Kel. Karet Kuningan, Kec. Setiabudi, Kota Adm. Jakarta Selatan, Prov. DKI Jakarta
INDIA - H.No. 8-2-699/1, SyNo. 346, Rd No. 12, Banjara Hills, Hyderabad, Telangana - 500034
SINGAPORE - 60 Paya Lebar Road #05-16, Paya Lebar Square, Singapore (409051)
USA - 251, Little Falls Drive, Wilmington, Delaware 19808
VIETNAM (Office 1) - Hung Vuong Building, 670 Ba Thang Hai, ward 14, district 10, Ho Chi Minh City
VIETNAM (Office 2) - 143 Nguyễn Thị Thập, Khu đô thị Him Lam, Quận 7, Thành phố Hồ Chí Minh 700000, Vietnam
Dubai - BrightChamps, 8W building 5th Floor, DAFZ, Dubai, United Arab Emirates
UK - Ground floor, Redwood House, Brotherswood Court, Almondsbury Business Park, Bristol, BS32 4QW, United Kingdom