Square Root of 676 + Solution With Free Steps

Square Root Of 676

26 is the square root of 676. The square of 676 is 676. 676 is a perfect square because its square root, 26, is a rational number rather than an integer. We might also state that 26 x26 = 676 since squares and square roots are the antithesis of one another.

In this article, we will analyze and find the square root of 676 using various mathematical techniques, such as the approximation method and the long division method.

What Is the Square Root Of 676?

The square root of the number 676 is 26.

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:

√676 = √(26 x 26)

√X = √(26)$^2$

√X = ±26

The square can be canceled with the square root as it is equivalent to 1/2; therefore, obtaining 26. Hence 26 is 676’s square root. The square root generates both positive and negative integers.

How To Calculate the Square Root of 676?

You can calculate the square root of 676 using any of two vastly used techniques in mathematics; one is the Approximation technique, and the other is the Long Division method.

The symbol √ is interpreted as 676 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 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 676 using the long division method:

Step 1

First, write the given number 676 in the division symbol, as shown in figure 1.

Step 2

Starting from the right side of the number, divide the number 676 into pairs such as 67 and 6.

Step 3

Now divide the digit 6 by a number, giving a number either 2 or less than 2. Therefore, in this case, the remainder is 2  whereas the quotient is 2.

Step 4

After this, bring down the next pair 76. Now the dividend is 276. To find the next divisor, we need to double our quotient obtained before. Doubling 2 gives 4; hence consider it as the next divisor.

Step 5

Now pair 2 with another number to make a new divisor that results in $\leq$ 276 when multiplied with the divisor. If the number is not a perfect square, add pair of zeros to the right of the number before starting division.

Step 6

Adding6 to the divisor and multiplying 46 with 6results in 276 = 276. The remainder obtained is 0. 

Step 7

The resulting quotient 26 is the square root of 676. Figure 1 given below shows the long division process in detail:

Square root of 676 by Long Division

Figure 1

Important points

  • The number 676 is a perfect square.
  • The number 676 is a rational number.
  • The number 676 can be split into its prime factorization.

Is Square Root of 676 a Perfect Square?

The number 676 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 676 is concerned, it is a perfect square. It can be proved as below:

Factorization of 676 results in 26 x 26 that can also be expressed as 26$^2$.

Taking the square root of the above expression gives:

= √(26$^2$)

= (26$^2$)$^{1/2}$

= 676

This shows that 676 is a perfect square and a rational number.

Therefore the above discussion proves that the square root of 676 is equivalent to 26.

Square root of 676 Calculation

Images/mathematical drawings are created with GeoGebra.

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