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Last updated on December 2nd, 2024

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Square Root of 2

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The square root of 2 is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is 2. The number 2 has a unique non-negative square root, called the principal square root.

Square Root of 2 for Filipino Students
Professor Greenline from BrightChamps

What Is the Square Root of 2?

The square root of 2 is ±1.41421356237, where is 1.41421356237 the positive solution of the equation x2 = 2.  

 

Finding the square root is just the inverse of squaring a number and hence, squaring 1.41421356237 will result in 2.

 

The square root of 2 is written as √2 in radical form, where the ‘√’  sign is called the “radical”  sign. In exponential form, it is written as (2)1/2 .

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Finding the Square Root of 2

We can find the square root of 2 through various methods. They are:
i) Prime factorization method
ii) Long division method
iii) Approximation/Estimation method
 

Professor Greenline from BrightChamps

Square Root of 2 By Prime Factorization Method

The prime factorization of 2 is done by dividing 2 by prime numbers and continuing to divide the quotients until they can’t be separated anymore.

 

After factorizing 2, make pairs out of the factors to get the square root. If there exist numbers that cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs.

 

So, Prime factorization of 2 = 2 × 1   
But here in the case of 2, no pairs of factors can be obtained but a single 2 is remaining

 

So, it can be expressed as  √2 
√2 is the simplest radical form.

 

Professor Greenline from BrightChamps

Square Root of 2 By Long Division Method


This method is 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 2:


 Step 1: Write the number 2, and draw a bar above the pair of digits from right to left.


               
Step 2: Now, find the greatest number whose square is less than or equal to. Here, it is
               1, Because 12=1 < 2.

 


Step 3 : Now divide 2 by 1 (the number we got from Step 2) such that we get 1 as quotient
             and we get a remainder. 

 

Double the divisor 1, we get 2, and then the largest possible number A1=4 is chosen such that when 4 is written beside the new divisor, 2, a 2-digit number is formed →24, and multiplying 4 with 24 gives 96 which is less than 100.

 

 Repeat the process until you reach the remainder of 0. We are left with the remainder, 3836 (refer to the picture), after some iterations and keeping the division till here, at this point.


             
Step 4 : The quotient obtained is the square root. In this case, it is 1.4142….

 


Professor Greenline from BrightChamps

Square Root of 2 By Approximation

Approximation or estimation of the square root is not the exact square root, but it is an estimate.

Here, through this method, an approximate value of square root is found by guessing.

Follow the steps below:

 


Step 1:  identify the square roots of the perfect squares above and below 2
             Below : 1→ square root of 1 = 1     ……..(i)
             Above : 4 →square root of 4 = 2     ……..(ii)

 


Step 2: Dividing 2 with one of 1 or 2      
             If we choose 1 
            We get 2 when 2 is divided by 1    …….(iii)


             
Step 3: Find the average of 1 (from (i)) and 2 (from (iii))
            (1+2)/2 = 1.5 

 

         
 Hence, 1.5 is the approximate square root of 2

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Common Mistakes and How to Avoid Them in the Square Root of 2

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Square Root of 2 Examples

Ray, the Character from BrightChamps Explaining Math Concepts
Max, the Girl Character from BrightChamps

Problem 1

Find the value of 1/√2 in rationalized form.

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Explanation

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Problem 2

Find the length of a side of a square whose area is 2 cm².

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Explanation

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Problem 3

Simplify (√2 + √2) ⤫ √2.

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Explanation

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Problem 4

If y=√2, find y²

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Explanation

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Max, the Girl Character from BrightChamps

Problem 5

Calculate (√2/2 + √2/4)

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Explanation

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FAQs on 2 Square Root

1.What is the exact value of the square root of 2 in terms of radicals?

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2.Is the square root of 2 a whole number?

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3.Is 2 a perfect square or a non-perfect square?

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4.Is the square root of 2 a rational or irrational number?

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5.What is the principal square root of 2?

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6.Is the square root of 2 a real number ?

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7.How does learning Algebra help students in Philippines make better decisions in daily life?

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8.How can cultural or local activities in Philippines support learning Algebra topics such as Square Root of 2?

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9.How do technology and digital tools in Philippines support learning Algebra and Square Root of 2?

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10.Does learning Algebra support future career opportunities for students in Philippines?

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Professor Greenline from BrightChamps

Important Glossaries for Square Root of 2

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. 


2)Factorization   
Expressing the given expression as a product of its factors
Ex: 48=2 ⤬ 2 ⤬ 2 ⤬ 2 ⤬ 3

 

3) Prime Numbers 
Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,...


4)  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. 

 

5) 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.

Professor Greenline from BrightChamps

About BrightChamps in Philippines

At BrightChamps, we believe algebra is more than symbols—it’s a gateway to countless opportunities! Our mission is to support children across the Philippines in mastering key math skills, focusing today on the Square Root of 2 with an emphasis on understanding square roots—in a lively, fun, and easy-to-follow way. Whether your child is calculating the speed of a roller coaster at Enchanted Kingdom, tracking basketball scores, or managing their allowance to buy the latest gadgets, mastering algebra builds their confidence for daily challenges. Our hands-on lessons make learning simple and enjoyable. Since kids in the Philippines learn in different styles, we tailor our approach to each learner. From Manila’s busy streets to the beautiful islands of Palawan, BrightChamps brings math to life, making it exciting and relevant throughout the Philippines. Let’s make square roots a fun part of every child’s math journey!
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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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Fun Fact

: He loves to play the quiz with kids through algebra to make kids love it.

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