305 LearnersLast updated on May 26th, 2025
Square Root of 1
The square root of 1 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 1. The number 1 has a unique non-negative square root, called the principal square root.
What Is the Square Root of 1?
The square root of 1 is ±1. Basically, finding the square root is just the inverse of squaring a number and hence, squaring 1 will result in 1. The square root of 1 is written as √1 in radical form. In exponential form, it is written as (1)1/2
Finding the Square Root of 1
We can find the square root of 1 through various methods. They are:
- Prime factorization method
- Long division method
- Repeated subtraction method
Square Root of 1 By Prime Factorization Method
The prime factorization of 1 can be found by dividing the number by prime numbers and continuing to divide the quotients until they can’t be divided anymore.
Find the factors of 1.
So, 1 is already a prime number. Since there is no factor of 1, the square root is directly 1.
Square Root of 1 By Long Division Method
This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.
Follow the steps to calculate the square root of 1:
Step 1: Write the number 1 and draw a bar above the pair of digits from right to left.
1 is a 1-digit number, so just simply draw a bar above it.
Step 2: Now, find the greatest number whose square is less than or equal to 1. Here, it is 1 because 12=1
Step 3: Now divide 1 by 1 (the number we got from step 2) and we get a remainder 0.
Step 4: The quotient obtained is the square root. In this case, it is 1.
Square Root of 1 By Subtraction Method
We know that the sum of first n odd numbers is n2. We will use this fact to find square roots through repeated subtraction method. Likewise, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of number of steps required to obtain 0.
Here are the steps:
1−1=0 So, after one subtraction, you're at zero, meaning the square root is 1
Common Mistakes and How to Avoid Them in the Square Root of 1
When we find the square root of 1, we often make some key mistakes, especially when we solve problems related to that. So, let’s see some common mistakes and their solutions
Mistake 1
Misunderstanding symbol
Often when √1 is mistaken as 12 , we square the number 1 and the get the result as 1. So, understanding of symbol should be clear.
Square Root of 1 Examples
Problem 1
Find the radius of a circle whose area is 1π cm^2.
Given, the area of the circle = 1π cm2
Now, area = πr2 (r is the radius of the circle)
So, πr2 = 1π cm2 ,
We get, r2 = 1 cm2 ,
r = √1 cm
Putting the value of √1 in the above equation,
We get, r = ±1 cm
Here we will consider the positive value of 1.
Therefore, the radius of the circle is 1 cm.
Answer: 1 cm.
Explanation
We know that, area of a circle = πr2 (r is the radius of the circle) According to this equation, we are getting the value of “r” as 1 cm by finding the value of the square root of 1
Problem 2
Find the length of a side of a square whose area is 1 cm^2 ?
Given, the area = 1 cm2,
We know that, (side of a square)2 = area of square
Or, (side of a square)2 = 1
Or, (side of a square)= √1
Or, side of a square = ± 1.
But, length of a square is a positive quantity only, so, length of the side is 1 cm.
Answer: 1 cm
Explanation
We know that, (side of a square)2 = area of square. Here, we are given with the area of the square, so, we can easily find out its square root because its Square root is the measure of the side of the square
Problem 3
√1 × √1, √1+√1
√1 × √1
= √(1 × 1) × √(1 × 1)
= 1 × 1
= 1
√1+√1
= √(1 × 1) + √(1 ×1)
= 1 + 1
= 2
Answer: 1, 2
Explanation
In the first expression, we multiplied the value of the square root of 1 with itself. In the second expression, we added the value of the square root of 1 with itself.
Problem 4
If y=√1, find y^2
firstly, y=√1= 1
Now, squaring y, we get,
y2=12=1
or, y2=1
Answer : 1
Explanation
squaring “y” which is same as squaring the value of √1 resulted to 1.
Problem 5
Calculate (√(1/100) + √(1/25))
√(1/100) + √(1/25)
= 1/10 + 1/5
= 0.1 + 0.2
= 0.3
Answer : 0.3
Explanation
From the given expression, we first found the value of square root of 1,100 and 25 then solved by simple divisions and then simple addition
FAQs on 1 Square Root
1.Can the square root of 1 be negative?
2.How do you find the square root of 1?
3.Is 1 a perfect square or non-perfect square?
4.Is the square root of 1 a rational or irrational number?
5.What is the square root of -1?
Important Glossaries for Square Root of 1
- Exponential form: An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 ×2 × 2 = 16 Or, 2 4 = 16, where 2 is the base, 4 is the exponent.
- Prime Factorization: Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3
- Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....
- Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers.
- Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24
- Imaginary numbers: It is the product of a real number and the imaginary unit “i”, where i is defined as i2= -1.
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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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