Square Root of 1681
The square root of a number is the value which, when multiplied by itself, gives the original number. e.g. 10 × 10 = 100; the square root of 100 is 10. Similarly, 1681 is a perfect square number. The square root of 1681 will be a number whose product with itself will result in 1681. The mathematical operation of square root is the inverse of a square. The square root of a number can be positive or negative, rational or irrational, real or imaginary. In this minilesson, we will calculate the square root of 1681 using different methods and we will look at some interesting problems related to it. 1681 is a perfect square number which can be obtained by the square of 41. Hence, the square root of 1681 is a rational number. In this minilesson, we will learn to find the square root of 1681 along with solved examples. Let us now find the square root of 1681.
 Square Root of 1681: √1681 = 41
 Square of 1681: 1681^{²} = 28,25,761
1.  What Is the Square Root of 1681? 
2.  Is Square Root of 1681 Rational or Irrational? 
3.  How to Find the Square Root of 1681? 
4.  FAQs on Square Root of 1681 
5.  Important Notes 
What Is the Square Root of 1681?
The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. We know that addition has an inverse operation which is subtraction and multiplication has an inverse operation which is division. Similarly, calculating the square root of a number is the inverse operation of squaring that number. The square root of 1681 is the number which, when multiplied to itself, will give the number 1681 as the result. Thus, we need to think of a number whose square is 1681.
 Square root of 1681 is written as √1681 (Radical form)
 Square root of 1681 = √1681 = √(41 × 41) = +41 and 41
 In the exponential form, the square root of 1681 is expressed as (1681)^{1/2}
The square root of 1681 is 41.
Is the Square Root of 1681 Rational or Irrational?
A rational number is a number that can be expressed in the form of p/q. A number that is not a rational number is called an irrational number. Nonterminating decimals which have repeated numbers after the decimal point are rational numbers. Now, let us look at the square root of 1681. 1681 can be broken into two factors which on multiplying give 1681. It can be written as a square of 41, which is a rational number. This shows that 1681 is a perfect square number.
 1681 is a number that is a perfect square because it has a natural number as its square root.
 Square root of 1681 is 41
 Square root of 1681 can be expressed as a fraction of the form p/q which tells us that the square root of 1681 is a rational number.
 The square root of 1681 is either +41 or 41.
 41 and 41 can be expressed as 41/1 and 41/1. Both the numbers can be represented in the form of a rational number. Thus, the square root of 1681 is a rational number.
How to Find the Square Root of 1681?
The square root of 1681 can be calculated using different methods such as: prime factorization and long division method. Since 1681 is a perfect square, we can use the repetitive subtraction method as well.
Let us calculate the square root of 1681 using long division method.
Square Root of 1681 by Long Division Method
 Step 1. Write 1681 as shown in the figure. Start grouping the number in pairs from the right. 81 is the first pair from the right and the next pair is 16.
 Step 2: Find the largest number that when multiplied with itself will give 16 or a smaller number closest to 16. Here it is 4 (4 × 4 = 16, remainder = 0).
 Step 3: Bring down the next pair of numbers. Here it is 81. The new divisor is 81 and the dividend is 81.
 Step 4: Find the largest number that when kept at ones place with 8 at tens place multiplied with that same number gives 81 as the result or a number closest to 81.
 Step 5: 1 is the next quotient place. Now we get our new divisor as 81 as 81 × 1 = 81. Complete the division and get the remainder. We get 0 as the remainder. Thus, the process of division completes here.
Therefore, the square root of 1681 = 41.
Explore square roots using illustrations and interactive examples
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Important Notes:
 The square root of 1681 is represented as √1681 in radical form.
 The square root of 1681 is represented as (1681)^{1/2} in exponential form.
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits.
Solved Examples

Example 1: The area of a squareshaped land is 1681 square units. Calculate the length of one side of the land.
Solution:
The area of the land = 1681 sq. units
To find the side of the squareshaped land, let us take the square root of 1682 by prime factorization method. Step 1. Prime factorization of 1681 = 1 × 41 × 41
 Step 2. Group the prime factors obtained for 1681 in pairs.
 Step 3. Pick one factor from each pair and they can be written in the form: 1681 = 41^{2}
 Step 4. Thus, following the law of exponents, we get, √1681 = √(41^{²}) = 41
Thus, we have √1681 = + 41 or 41
Therefore, the length of one side of the square land is 41 units.

Example 2: Sherin has a square mat that has an area of 1681 square inches. The mat has embroidery on its borders. The interior area of the mat is 1024 square inches. Can you calculate the width of the embroidery on the mat?
Solution:
We know that the length of each side of the mat = √1681 = 41 inches
Length of the interior of the mat = √1024 = 32 inches
Thus, width of the embroidery = 41  32 = 9 inches
FAQs on Square Root of 1681
What is the square root of 1681 using prime factorization?
Prime factorization of 1681 = 1 × 41 × 41
Pick one factor from each pair and they can be written as √1681 = 41
Is 1681 a perfect square?
1681 is a perfect square. 1681 is a natural number. Since there is another natural number that can be squared to result in the number 1681, i.e., 41, it is a perfect square.
What is the value of √1681 times √1681?
The value of the √1681 × √1681 is 1681.
Is the square root of 1681 a rational number?
Yes, the square root of 1681 is a rational number since the square root of 1681 can be represented in the form of p/q.
Can we find the square root of 1681 by the repeated subtraction method?
Yes, we can find the square root of 1681 by the repeated subtraction method as it can be used only for perfect squares. 1681 is a perfect square.
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