114 LearnersLast updated on May 26th, 2025
Square of 85
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 85.
What is the Square of 85
The square of a number is the product of the number with itself. The square of 85 is 85 × 85. The square of a number always ends in 0, 1, 4, 5, 6, or 9. We write it in math as 85², where 85 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 85 is 85 × 85 = 7225. Square of 85 in exponential form: 85² Square of 85 in arithmetic form: 85 × 85
How to Calculate the Value of Square of 85
The square of a number is calculated by multiplying the number by itself. 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 85 Step 1: Identify the number. Here, the number is 85 Step 2: Multiply the number by itself, we get, 85 × 85 = 7225. The square of 85 is 7225.
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: Identify the number and substitute the value in the equation. Here, ‘a’ is 85 So: 85² = 85 × 85 = 7225
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 85. Step 1: Enter the number in the calculator Enter 85 in the calculator. Step 2: Multiply the number by itself using the multiplication button (×) That is 85 × 85 Step 3: Press the equal button to find the answer Here, the square of 85 is 7225. Tips and Tricks for the Square of 85 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 85
Mistakes are common among learners when doing math, especially when it involves finding the square of a number. Let’s learn some common mistakes to master squaring a number.
Mistake 1
Calculation errors:
Calculation errors mostly happen when students skip steps or swap the digits. To avoid this, students should double-check their answers. 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. Students may mistakenly use 85² with (8 + 5)² or (80 + 5)². Students should check and use the correct formula and double-check their answers to avoid confusion.
Mistake 3
Confusing square with square root.
Not understanding the concept of square and square root can lead to confusion. To avoid this, students should understand 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 parentheses when finding the square of a number can lead to errors. 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 squaring a number. Students should practice regularly to avoid errors.
Solved Examples on Square of 85
Problem 1
Find the length of a square, where the area of the square is 7225 cm².
The area of a square = a² So, the area of the square = 7225 cm² So, the length = √7225 = 85. The length of each side = 85 cm
Explanation
The length of a square is 85 cm. Because the area is 7225 cm², the length is √7225 = 85.
Problem 2
Anna wants to tile her square patio, which has a side length of 85 feet. The cost to tile a square foot is 5 dollars. How much will it cost to tile the entire patio?
The length of the patio = 85 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 = 85 Therefore, the area of the patio = 85² = 85 × 85 = 7225. The cost to tile the patio = 7225 × 5 = 36125. The total cost = 36125 dollars
Explanation
To find the cost to tile the patio, we multiply the area of the patio by the cost per square foot. So, the total cost is 36125 dollars.
Problem 3
Find the area of a circle whose radius is 85 meters.
The area of the circle = 22698.66 m²
Explanation
The area of a circle = πr² Here, r = 85 Therefore, the area of the circle = π × 85² = 3.14 × 85 × 85 = 22698.66 m².
Problem 4
The area of the square is 7225 cm². Find the perimeter of the square.
The perimeter of the square is
Explanation
The area of the square = a² Here, the area is 7225 cm² The length of the side is √7225 = 85 Perimeter of the square = 4a Here, a = 85 Therefore, the perimeter = 4 × 85 = 340.
Problem 5
Find the square of 86.
The square of 86 is 7396
Explanation
The square of 86 is multiplying 86 by 86. So, the square = 86 × 86 = 7396
FAQs on Square of 85
1.What is the square of 85?
2.What is the square root of 85?
3.Is 85 a prime number?
4.What are the first few multiples of 85?
5.What is the square of 84?
6.How does learning Algebra help students in United Arab Emirates make better decisions in daily life?
7.How can cultural or local activities in United Arab Emirates support learning Algebra topics such as Square of 85?
8.How do technology and digital tools in United Arab Emirates support learning Algebra and Square of 85?
9.Does learning Algebra support future career opportunities for students in United Arab Emirates?
Important Glossaries for Square 85.
Prime number: A prime number is a number that is only divisible by 1 and itself. For example, 2, 3, 5, 7, etc. Exponential form: Exponential form is a way of writing numbers using bases and exponents, such as 9². Square root: The square root is the inverse operation of the square. The square root of a number is a value that, when multiplied by itself, gives the original number. Perfect square: A perfect square is a number that has an integer as its square root. For example, 36 is a perfect square because its square root is 6. Odd number: An odd number is a number that is not divisible by 2. For example, 1, 3, 5, 7, etc.
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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.
