Last updated on May 26th, 2025
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.
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
We can find the square root of 1 through various methods. They are:
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.
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.
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
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
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.
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
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
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
√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
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.
If y=√1, find y^2
firstly, y=√1= 1
Now, squaring y, we get,
y2=12=1
or, y2=1
Answer : 1
squaring “y” which is same as squaring the value of √1 resulted to 1.
Calculate (√(1/100) + √(1/25))
√(1/100) + √(1/25)
= 1/10 + 1/5
= 0.1 + 0.2
= 0.3
Answer : 0.3
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
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.
: He loves to play the quiz with kids through algebra to make kids love it.