122 LearnersLast updated on May 26th, 2025
Square of 169
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 the topic, we will discuss the square of 169.
What is the Square of 169
The square of a number is the product of the number itself. The square of 169 is 169 × 169. The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 169², where 169 is the base and 2 is the exponent. The square of a positive and a negative number is always positive. For example, 5² = 25; -5² = 25.
The square of 169 is 169 × 169 = 28561. Square of 169 in exponential form: 169² Square of 169 in arithmetic form: 169 × 169
How to Calculate the Value of Square of 169
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
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 169.
Step 1: Identify the number. Here, the number is 169
Step 2: Multiplying the number by itself, we get, 169 × 169 = 28561. The square of 169 is 28561.
Using a Formula (a²)
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 169 So: 169² = 169 × 169 = 28561
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 169.
Step 1: Enter the number in the calculator Enter 169 in the calculator.
Step 2: Multiply the number by itself using the multiplication button(×) That is 169 × 169
Step 3: Press the equal to button to find the answer Here, the square of 169 is 28561.
Tips and Tricks for the Square of 169 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, √1.44 = 1.2 The square root of a perfect square is always a whole number. For example, √144 = 12.
Common Mistakes to Avoid When Calculating the Square of 169
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
Calculation errors:
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.
Mistake 2
Errors while using the formula.
The formula to find the square of the number is a². Instead, students may use 169² with (1+6+9)² or (100+69)². So students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing with square and square root.
Not understanding the concept of square and square root can lead to confusion in students. To avoid it, students should understand the concept that square and square root are inverse operations. The square of 5 is 25 and the square root of 25 is ±5.
Mistake 4
Errors in parentheses.
Ignoring the parentheses when finding the square of a number can lead to errors. So, students should understand parentheses. And do the operations in the correct order to avoid errors.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. So students should do regular practice to avoid errors.
Solved Examples on Square of 169
Problem 1
Find the length of the square, where the area of the square is 28561 cm².
The area of a square = a² So, the area of a square = 28561 cm² So, the length = √28561 = 169. The length of each side = 169 cm
Explanation
The length of a square is 169 cm.
Because the area is 28561 cm² the length is √28561 = 169.
Problem 2
Sarah is planning to tile her square garden of length 169 feet. The cost to tile a foot is 5 dollars. Then how much will it cost to tile the full garden?
The length of the garden = 169 feet The cost to tile 1 square foot of garden = is 5 dollars. To find the total cost to tile, we find the area of the garden, Area of the garden = area of the square = a² Here a = 169 Therefore, the area of the garden = 169² = 169 × 169 = 28561. The cost to tile the garden = 28561 × 5 = 142805. The total cost = 142805 dollars
Explanation
To find the cost to tile the garden, we multiply the area of the garden by cost to tile per foot.
So, the total cost is 142805 dollars.
Problem 3
Find the area of a circle whose radius is 169 meters.
The area of the circle = 89617.24 m²
Explanation
The area of a circle = πr²
Here, r = 169
Therefore, the area of the circle = π × 169²
= 3.14 × 169 × 169
= 89617.24 m².
Problem 4
The area of the square is 28561 cm². Find the perimeter of the square.
The perimeter of the square is 676 cm.
Explanation
The area of the square = a²
Here, the area is 28561 cm²
The length of the side is √28561 = 169
Perimeter of the square = 4a
Here, a = 169
Therefore, the perimeter = 4 × 169 = 676.
Problem 5
Find the square of 170.
The square of 170 is 28900.
Explanation
The square of 170 is multiplying 170 by 170.
So, the square = 170 × 170 = 28900.
FAQs on Square of 169
1.What is the square of 169?
2.What is the square root of 169?
3.Is 169 a prime number?
4.What are the first few multiples of 169?
5.What is the square of 168?
6.How does learning Algebra help students in United Kingdom make better decisions in daily life?
7.How can cultural or local activities in United Kingdom support learning Algebra topics such as Square of 169?
8.How do technology and digital tools in United Kingdom support learning Algebra and Square of 169?
9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Square 169.
- Perfect Square: A number that is the square of an integer. For example, 16 is a perfect square of 4.
- Exponential form: Exponential form is the way of writing a number in the form of a power. For example, 9² where 9 is the base and 2 is the power.
- 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.
- Area: The measurement of the surface of a shape. For example, the area of a square is side × side.
- Perimeter: The total distance around the edge of a shape. For example, the perimeter of a square is 4 times the length of one side.
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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.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
