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Last updated on May 26th, 2025

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Square of 688

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The product of multiplying an integer by itself is the square of a number. Square is used in programming, calculating areas, and so on. In this topic, we will discuss the square of 688.

Square of 688 for Singaporean Students
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What is the Square of 688

The square of a number is the product of the number itself. The square of 688 is 688 × 688. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as (6882), where 688 is the base and 2 is the exponent. The square of a positive and a negative number is always positive.

For example, (52 = 25); ((-5)2 = 25).

The square of 688 is 688 × 688 = 473,344.

Square of 688 in exponential form: (6882)

Square of 688 in arithmetic form: 688 × 688

Square of 688

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How to Calculate the Value of Square of 688

The square of a number is multiplying the number by itself. So let’s learn how to find the square of a number. These are the common methods used to find the square of a number.

 

  • By Multiplication Method
  • Using a Formula
  • Using a Calculator
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By the Multiplication method

In this method, we will multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 688.

 

Step 1: Identify the number. Here, the number is 688.

 

Step 2: Multiplying the number by itself, we get, 688 × 688 = 473,344.

 

The square of 688 is 473,344.

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Using a Formula (\(a^2\))

In this method, the formula, (a2) is used to find the square of the number, where (a) is the number.

 

Step 1: Understanding the equation

Square of a number = (a2)

(a2 = a × a)

 

Step 2: Identifying the number and substituting the value in the equation.

Here, ‘a’ is 688.

So: (6882 = 688 × 688 = 473,344\)

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By Using a Calculator

Using a calculator to find the square of a number is the easiest method. Let’s learn how to use a calculator to find the square of 688.

 

Step 1: Enter the number in the calculator Enter 688 in the calculator.

 

Step 2: Multiply the number by itself using the multiplication button(×) That is 688 × 688

 

Step 3: Press the equal to button to find the answer Here, the square of 688 is 473,344.

 

Tips and Tricks for the Square of 688

 

Tips and tricks make it easy for students to understand and learn the square of a number. To master the square of a number, these tips and tricks will help students.

 

  • The square of an even number is always an even number. For example, (62 = 36)
     
  • The square of an odd number is always an odd number. For example, (52 = 25)
     
  • The last digit of the square of a number is always 0, 1, 4, 5, 6, or 9.
     
  • If the square root of a number is a fraction or a decimal, then the number is not a perfect square. For example, (sqrt{1.44} = 1.2)
     
  • The square root of a perfect square is always a whole number. For example, (sqrt{144} = 12).
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Common Mistakes to Avoid When Calculating the Square of 688

Mistakes are common among kids when doing math, especially when it is finding the square of a number. Let’s learn some common mistakes to master the squaring of a number.

Mistake 1

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Calculation errors:

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Calculation errors mostly happen when students skip the steps or else by swapping the digits. To avoid it, students should double-check the answer. They can double-check by finding the square root of the solution they found.

 

For example, the square of 25 is 625, and the square root of 625 is ±25.

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Solved Examples on Square of 688

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Problem 1

Find the length of the square, where the area of the square is 473,344 cm².

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The area of a square = (a2)

So, the area of a square = 473,344 cm²

So, the length = (sqrt{473,344} = 688).

The length of each side = 688 cm

Explanation

The length of a square is 688 cm. Because the area is 473,344 cm² the length is (sqrt{473,344} = 688).

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Problem 2

Sarah is planning to carpet her square room of length 688 feet. The cost to carpet a foot is 5 dollars. Then how much will it cost to carpet the full room?

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The length of the room = 688 feet

The cost to carpet 1 square foot of the room = 5 dollars.

To find the total cost to carpet, we find the area of the room,

Area of the room = area of the square = (a2)

Here a = 688

Therefore, the area of the room = (6882 = 688 × 688 = 473,344).

The cost to carpet the room = 473,344 × 5 = 2,366,720.

The total cost = 2,366,720 dollars

Explanation

To find the cost to carpet the room, we multiply the area of the room by cost to carpet per foot. So, the total cost is 2,366,720 dollars.

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Problem 3

Find the area of a circle whose radius is 688 meters.

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The area of the circle = 1,487,949.76 m²

Explanation

The area of a circle = πr²

Here, r = 688

Therefore, the area of the circle = π × 688²

= 3.14 × 688 × 688

= 1,487,949.76 m².

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Problem 4

The area of the square is 473,344 cm². Find the perimeter of the square.

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The perimeter of the square is 2,752 cm.

Explanation

The area of the square = (a2)

Here, the area is 473,344 cm²

The length of the side is (sqrt{473,344} = 688)

Perimeter of the square = 4a

Here, a = 688

Therefore, the perimeter = 4 × 688 = 2,752 cm.

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Problem 5

Find the square of 689.

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The square of 689 is 474,721.

Explanation

The square of 689 is multiplying 689 by 689. So, the square = 689 × 689 = 474,721.

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FAQs on Square of 688

1.What is the square of 688?

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2.What is the square root of 688?

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3.Is 688 a prime number?

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4.What are the first few multiples of 688?

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5.What is the square of 687?

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

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7.How can cultural or local activities in Singapore support learning Algebra topics such as Square of 688?

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8.How do technology and digital tools in Singapore support learning Algebra and Square of 688?

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

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Important Glossaries for Square 688.

  • Prime Number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, etc.

     
  • Exponential Form: A way of writing numbers using a base and an exponent. For example, (92) where 9 is the base and 2 is the exponent.

     
  • Square Root: The square root is the inverse operation of the square. The square root of a number is a number whose square is the number itself.

     
  • Even Number: A number divisible by 2 without a remainder. For example, 2, 4, 6, etc.

     
  • Area: The measure of the extent of a two-dimensional figure or shape in a plane. For example, the area of a square is (a2) where a is the length of the side.
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About BrightChamps in Singapore

At BrightChamps, algebra is more than just symbols—it’s a gateway to endless possibilities! Our goal is to help kids all over Singapore strengthen their math skills, with today’s lesson centered on the Square of 688 and a special focus on understanding squares—in a fun, engaging, and easy-to-follow way. Whether your child is timing a roller coaster at Universal Studios Singapore, keeping score at a local football match, or managing their allowance for the latest gadgets, algebra helps boost their confidence in daily life. Our lessons are designed to make learning simple and enjoyable. Since kids in Singapore learn in many different ways, we personalize our approach for each child. From the bustling city to the scenic gardens, BrightChamps brings math to life, making it relatable and exciting throughout Singapore. Let’s make squares an enjoyable part of every child’s math journey!
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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.

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Fun Fact

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

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