119 LearnersLast updated on May 26th, 2025
Square of 172
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 172.
What is the Square of 172
The square of a number is the product of the number itself. The square of 172 is 172 × 172. The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 172², where 172 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 172 is 172 × 172 = 29584. Square of 172 in exponential form: 172² Square of 172 in arithmetic form: 172 × 172
How to Calculate the Value of Square of 172
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 172.
Step 1: Identify the number. Here, the number is 172.
Step 2: Multiplying the number by itself, we get, 172 × 172 = 29584. The square of 172 is 29584.
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 172. So: 172² = 172 × 172 = 29584
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 172.
Step 1: Enter the number in the calculator Enter 172 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 172 × 172.
Step 3: Press the equal to button to find the answer Here, the square of 172 is 29584.
Tips and Tricks for the Square of 172 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 172
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 when using the formula.
The formula to find the square of the number is a². Instead, students may use 172² with (1 + 7 + 2)² or (170 + 2)². So students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing square with 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 perform 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 172
Problem 1
Find the side length of a square, where the area of the square is 29584 cm².
The area of a square = a² So, the area of the square = 29584 cm² So, the side length = √29584 = 172. The length of each side = 172 cm
Explanation
The length of a square is 172 cm because the area is 29584 cm²
so the length is √29584 = 172.
Problem 2
Sarah is planning to tile her square patio of side length 172 feet. The cost to tile a square foot is 5 dollars. How much will it cost to tile the entire patio?
The side length of the patio = 172 feet The cost to tile 1 square foot of the patio = 5 dollars. To find the total cost to tile, we find the area of the patio, Area of the patio = area of the square = a² Here a = 172 Therefore, the area of the patio = 172² = 172 × 172 = 29584. The cost to tile the patio = 29584 × 5 = 147920. The total cost = 147920 dollars.
Explanation
To find the cost to tile the patio, we multiply the area of the patio by the cost to tile per foot.
So, the total cost is 147920 dollars.
Problem 3
Find the area of a circle whose radius is 172 meters.
The area of the circle = 92948.64 m²
Explanation
The area of a circle = πr²
Here, r = 172
Therefore, the area of the circle = π × 172²
≈ 3.14 × 172 × 172
= 92948.64 m².
Problem 4
The area of the square is 29584 cm². Find the perimeter of the square.
The perimeter of the square is 688 cm.
Explanation
The area of the square = a²
Here, the area is 29584 cm²
The side length is √29584 = 172.
Perimeter of the square = 4a
Here, a = 172
Therefore, the perimeter = 4 × 172 = 688.
Problem 5
Find the square of 173.
The square of 173 is 29929.
Explanation
The square of 173 is found by multiplying 173 by 173.
So, the square = 173 × 173 = 29929.
FAQs on Square of 172
1.What is the square of 172?
2.What is the square root of 172?
3.Is 172 a prime number?
4.What are the first few multiples of 172?
5.What is the square of 171?
6.How does learning Algebra help students in Singapore make better decisions in daily life?
7.How can cultural or local activities in Singapore support learning Algebra topics such as Square of 172?
8.How do technology and digital tools in Singapore support learning Algebra and Square of 172?
9.Does learning Algebra support future career opportunities for students in Singapore?
Important Glossaries for Square of 172
- Prime number: A number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, 11, etc.
- Exponential form: A way of writing a number as a base raised to a power, e.g., 9² where 9 is the base and 2 is the exponent.
- Square root: The square root of a number is a value that, when multiplied by itself, gives the original number.
- Perfect square: A number that is the square of an integer. For example, 144 is a perfect square because it is 12².
- Even number: A number that is divisible by 2. For example, 2, 4, 6, 8, etc.
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About BrightChamps in Singapore
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.
