Square Root of 1681 + Solution With Free Steps

The square root of the number 1681 is a perfect square number. The perfect square number is the one in which there are no decimal places we said that number to be a perfect square number. Like in this case the square root of 1681 is equal to √1681=41. If the number is perfect square it is also said to be rational. 

In this article, we will analyze and find the square root of 1681 using various mathematical techniques, such as the long division method.

What Is the Square Root Of 1681?

The square root of the number 1681 is 41.

The square root can be defined as the quantity that can be doubled to produce the square of that similar quantity. In simple words, it can be explained as:

√1681 = √(41 x 41)

√1681 = √(41)$^2$

√1681 = ±41

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 41. Hence 41 is 1681’s square root. The square root generates both positive and negative integers.

How To Calculate the Square Root of 1681?

You can calculate the square root of 1681 using techniques in mathematics such as the Long Division method.

The symbol √ is interpreted as 1681 raised to the power 1/2. So any number, when multiplied by itself, produces its square, and when the square root of any squared number is taken, it produces the actual number.

Let us discuss each of them to understand the concepts better.

Square Root of 1681 by Long Division Method

The process of long division is one of the most common methods used to find the square roots of a given number. It is easy to comprehend and provides more reliable and accurate answers. The long division method reduces a multi-digit number to its equal parts.

Learning how to find the square root of a number is easy with the long division method. All you need are five primary operations- divide, multiply, subtract, bring down or raise, then repeat.

Following are the simple steps that must be followed to find the square root of 1681 using the long division method:

Step 1

First, write the given number 1681 in the division symbol, as shown in figure 1.

Step 2

Starting from the right side of the number, divide the number 1681 into pairs such as 81 and 16.

Step 3

Now divide the digit 16 by a number, giving a number either 16 or less than 16. Therefore, in this case, the remainder is zero, whereas the quotient is 4.

Step 4

After this, bring down the next pair 81. Now the dividend is 81. To find the next divisor, we need to double our quotient obtained before. Doubling 4 gives 8; hence consider it as the next divisor.

Step 5

Now pair 8 with another number to make a new divisor that results in $\leq$ 81 when multiplied with the divisor. 

Step 6

Adding 81 to the divisor and multiplying 81 with 1 results in 81 $\leq$ 81. The remainder obtained is 0. 

Step 7

The resulting quotient 41 is the square root of 1681. Figure 1 given below shows the long division process in detail:

Important points

• The number 1681 is a perfect square.
• The number 1681 is a rational number.
• The number 1681 can be split into its prime factorization.

Is Square Root of 1681 a Perfect Square?

The number 1681 is a perfect square. A number is a perfect square if it splits into two equal parts or identical whole numbers. If a number is a perfect square, it is also rational.

A number expressed in p/q form is called a rational number. All the natural numbers are rational. A square root of a perfect square is a whole number; therefore, a perfect square is a rational number.

A number that is not a perfect square is irrational as it is a decimal number. As far as 1681 is concerned, it is a perfect square. It can be proved as below:

Factorization of 1681 results in 41 x 41 which can also be expressed as 41$^2$.

Taking the square root of the above expression gives:

= √(41$^2$)

= (41$^2$)$^{1/2}$

= 41

This shows that 1681 is a perfect square and a rational number.

Therefore the above discussion proves that the square root of 1681 is equivalent to 41.