How To Find The Square Root Of 676? - Cuemath

Square Root of 676

676 can be obtained by squaring 26. Hence, it is a perfect square number. Hence, the square root of 676 is a rational number. In this mini-lesson we will learn to find square root of 676 along with solved examples. Let us see what the square root of 676 is.

• Square Root of 676: √676 = 26
• Square of 676: 6762 = 4,56,976

1.	What Is the Square Root of 676?
2.	Is Square Root of 676 Rational or Irrational?
3.	How to Find the Square Root of 676?
4.	Important Notes
5.	Thinking Out of the Box!
6.	FAQs on Square Root of 676

What Is the Square Root of 676?

The number whose square is 676 is 26. Hence, the square root of 676 is 26. It is written as

√676 = 26

The answer which is obtained on squaring 26 is 676. Hence, 676 is a perfect square.

Is the Square Root of 676 Rational or Irrational?

As 676 is √676 = 26, it is possible to express √676 in p/q form easily. This makes √676 a rational number. 

How to Find the Square Root of 676?

There are different methods to determine the square root of any number. Click here to know more about it. We can determine the square root of 676 using two methods:

• Square Root of 676 by Long Division
• Square Root of 676 by Prime Factorization

Square Root of 676 by Long Division

The square root of 676 can be found using the long division as follows.

• Step 1: We pair digits of a given number starting with a digit at one's place. Put a horizontal bar to indicate pairing.
• Step 2: Now we find a number which on multiplication with itself gives a product less than or equal to 6. As we know 2 × 2 = 4 < 6. Hence, the divisor is 2 and the quotient is 2. 
• Step 3: Now, we have to bring down 00 and multiply the quotient by 2. This give us 4. Hence, 4 is the starting digit of the new divisor.
• Step 4: 6 is placed at one's place of new divisor because when 46 is multiplied by 6 we get 276. The obtained answer now is 0. Now the new divisor obtained is 52.
• Step 5: Hence, the square root of 676 is 26.

Square Root of 676 by Prime Factorization

676 is a perfect square hence, we can also express it as (2 × 2 × 13 × 13). The numbers within square root which get repeated are 2 and 13. Hence, the square root of 676 is 2 × 13 = 26 .

The square root of 676 is 26.

Explore square roots using illustrations and interactive examples

• Square Root of 169
• Square Root of 196
• Square Root of 225
• Square Root of 289
• Square Root of 400

Important Notes:

• 676 is a perfect square as the value obtained after taking its square root is a whole number.
• The square root of 676 can be simplified to 26 either by using the prime factorization of 676 or by expressing 676 as a square of 26.

Think Tank:

• Can the value of a square root of 676 be decimal?
• Are -√676 and √-676 same?