Square Root of 676

The square root of 676 is equal to 26, i.e. √676 = 26.

In mathematics, the square root of a number is a value that gives the actual number on multiplication by itself. Suppose x is the square root value of y such that it can be shown as x = √y and x² = y, where the radical symbol “√” denotes the square root of numbers. When multiplied by itself, the positive number represents the square of the number. Thus, the square root of the square of a positive number gives the original number, i.e. √(p²) = p, where p² is the square of p. In this article, you will learn how to estimate the square root of 676 using different methods, such as repeated subtraction, long division along with solved examples.

What is the Square Root of 676?

The square root of 676 is 26, i.e. √676 = 26. The radical representation of the square root of 676 is √676. Also, we know that the square of 26 is 676, i.e. 26² = 26 × 26 = 676. Thus, the square root of 676 can also be expressed as, √676 = √(26)² = √(26 × 26) = 26. Also, we can say that 676 is a perfect square.

The square root of 676 can be both positive and negative of 26 since 26 × 26 = 676 and (-26) × (-26) = 676. Therefore, the square root of 676 is ±26. However, “the square root” is often used to refer to the principal or non-negative square root. Thus, we write the positive number as the result unless specified.

How to Calculate Square Root of 676

The different methods that can be used to find the square root of 676 are given below.

• Repeated subtraction
• Prime factorization
• Long division

Let’s understand how to calculate the square root of 676 using all these methods, one by one.

Square Root of 676 by Repeated Subtraction Method

In this method, we subtract the successive odd numbers till we obtain zero, starting from 676 and 1. The number of odd numbers we subtract in this process is treated as the square root of the number 676.

• 676 – 1 = 675
• 675 – 3 = 672
• 672 – 5 = 667
• 667 – 7 = 660
• 660 – 9 = 651
• 651 – 11 = 640
• 640 – 13 = 627
• 627 – 15 = 612
• 612 – 17 = 595
• 595 – 19 = 576
• 576 – 21 = 555
• 555 – 23 = 532
• 532 – 25 – 507
• 507 – 27 = 480
• 480 – 29 = 451
• 451 – 31 = 420
• 420 – 33 = 387
• 387 – 35 = 352
• 352 – 37 = 315
• 315 – 39 = 276
• 276 – 41 = 235
• 235 – 43 = 192
• 192 – 45 = 147
• 147 – 47 = 100
• 100 – 49 = 51
• 51 – 51 = 0

Thus, starting from 676, we have subtracted 26 consecutive odd numbers to get 0. Therefore, the square root of 676 is 26.

Learn more information about the square root of a number by the repeated subtraction method here.

Square Root of 676 by Prime Factorization Method

In the prime factorization method, we first find the prime factorization of 676.

The prime factorization of 676 = 2 × 2 × 13 × 13

This can be done by dividing the number 676 by prime numbers 2, 3, 5, etc. until we get the result 1 as a quotient.

Consider, 676 = 2 × 2 × 13 × 13

Now, take the square root on both sides.

√676 = √(2 × 2 × 13 × 13)

To get the square root value, we need to group the prime factors in pairs.

√676 = √[(2 × 2) × (13 × 13)]

√676 = 2 × 13 = 26

Hence, the square root of 676 is equal to 26.

Square Root of 676 by Long Division Method

Let’s have a look at the division method of estimating the square root of 676.

• Write 676.
• Take the digits of the number in pairs from the right. So, from 676, 76 is chosen as a pair, and 6 stand-alone.
• We need to divide 6 with a number such that the number × number gives 6 or a number less than that. In this case, 2 × 2 = 4, which is less than 6.
• Now, we get 2 as the quotient and 2 as the remainder.
• Let’s bring down 76 for division.
• Double the divisor, that means 2 + 2 = 4. Write this as one of the digits for the new divisor.
• Find a number that can be placed on the right side of 4 to obtain a two-digit number as a new divisor. Also, the number set here should be multiplied by itself to produce 276 or less than that.
• We find that 6 is the number such that 46 × 6 gives 276.
• Now we got the quotient 26 and the remainder as 0.

Get Square Root of More Numbers Here

Video Lessons on Square Roots

Visualising square roots

Finding Square roots

Solved Example

Question

If the area of a square-shaped field is 676 m², find the length of each side of the field.

Solution:

Given,

Area of field = 676 m²

We know that the area of a square of side “a” = a²

So, a² = 676

a = √676 = 26 {a cannot be -26 since the side measure cannot be negative}

Therefore, the length of each side of the square-shaped field is 26 m.