117 LearnersLast updated on May 26th, 2025
Square of 1013
The product of multiplying an integer by itself is the square of a number. Squares are used in programming, calculating areas, and so on. In this topic, we will discuss the square of 1013.
What is the Square of 1013
The square of a number is the product of the number by itself. The square of 1013 is 1013 × 1013. The square of a number often ends in 0, 1, 4, 5, 6, or 9. We write it in math as 1013², where 1013 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 1013 is 1013 × 1013 = 1,026,169.
Square of 1013 in exponential form: 1013²
Square of 1013 in arithmetic form: 1013 × 1013
How to Calculate the Value of Square of 1013
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 1013.
Step 1: Identify the number. Here, the number is 1013.
Step 2: Multiplying the number by itself, we get, 1013 × 1013 = 1,026,169.
The square of 1013 is 1,026,169.
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 1013.
So: 1013² = 1013 × 1013 = 1,026,169
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 1013.
Step 1: Enter the number in the calculator. Enter 1013 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 1013 × 1013.
Step 3: Press the equal button to find the answer. Here, the square of 1013 is 1,026,169.
Tips and Tricks for the Square of 1013
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 1013
Mistakes are common among students when doing math, especially when 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 in using the formula.
The formula to find the square of the number is a². Instead, students may use 1013² with (1000+13)² incorrectly. So students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing 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 error.
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 1013
Problem 1
Find the length of the square, where the area of the square is 1,026,169 cm².
The area of a square = a²
So, the area of a square = 1,026,169 cm²
So, the length = √1,026,169 = 1013.
The length of each side = 1013 cm
Explanation
The length of a square is 1013 cm. Because the area is 1,026,169 cm², the length is √1,026,169 = 1013.
Problem 2
Sarah wants to lay carpet on her square floor of length 1013 feet. The cost to carpet a foot is 5 dollars. Then how much will it cost to carpet the full floor?
The length of the floor = 1013 feet
The cost to carpet 1 square foot of floor = 5 dollars.
To find the total cost to carpet, we find the area of the floor,
Area of the floor = area of the square = a²
Here a = 1013
Therefore, the area of the floor = 1013²
= 1013 × 1013 = 1,026,169.
The cost to carpet the floor = 1,026,169 × 5 = 5,130,845.
The total cost = 5,130,845 dollars
Explanation
To find the cost to carpet the floor, we multiply the area of the floor by the cost to carpet per foot. So, the total cost is 5,130,845 dollars.
Problem 3
Find the area of a circle whose radius is 1013 meters.
The area of the circle = 3,225,033.02 m²
Explanation
The area of a circle = πr²
Here, r = 1013
Therefore, the area of the circle = π × 1013²
= 3.14 × 1013 × 1013
= 3,225,033.02 m².
Problem 4
The area of the square is 1026 cm². Find the perimeter of the square.
The perimeter of the square is 128 cm.
Explanation
The area of the square = a²
Here, the area is 1026 cm²
The length of the side is √1026 (which doesn't exactly match a whole number, but for example purposes, we assume it approximates to the context)
Perimeter of the square = 4a
Therefore, assuming a was found to be approximated at 32 for this example, the perimeter = 4 × 32 = 128 cm.
Problem 5
Find the square of 1014.
The square of 1014 is 1,028,196.
Explanation
The square of 1014 is found by multiplying 1014 by 1014.
So, the square = 1014 × 1014 = 1,028,196.
FAQs on Square of 1013
1.What is the square of 1013?
2.What is the square root of 1013?
3.Is 1013 a prime number?
4.What are the first few multiples of 1013?
5.What is the square of 1012?
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 1013?
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9.Does learning Algebra support future career opportunities for students in United Kingdom?
Important Glossaries for Square of 1013.
- Prime number: A prime number is any number that is only divisible by 1 and itself. Examples include 2, 3, 5, 7, 11, etc.
- Exponential form: Exponential form is a way of writing numbers using a base and an exponent. For example, 9², where 9 is the base and 2 is the exponent.
- Perfect Square: A perfect square is a number that is the square of an integer, such as 16 (4²) or 25 (5²).
- Square Root: The square root is the inverse operation of squaring a number. It represents a value that, when multiplied by itself, gives the original number.
- Radius: In geometry, the radius is the distance from the center of a circle to any point on its circumference.
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Jaskaran Singh Saluja
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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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