A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
LearnPracticeDownload

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 Long Division

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 .

Square Root of 676 by Prime Factorization

The square root of 676 is 26.

Explore square roots using illustrations and interactive examples

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? 
 

Square Root of 676 Solved Examples

  1. Example 1: Can you determine the difference in lengths of square boxes having area 676 square inches and 576 square inches?

    Solution

    As the area of square box is area = length × length
    The length of square box having area 676 square inches is √676 = 26 inches. 
    Similarly, the length of box having area 576 square inches is √576 = 24 inches.
    The difference in lengths of boxes is (26 - 24) inches = 2 inches

    Hence, the difference in length of square boxes having area 676 square inches and 576 square inches is 2 inches.

  2. Example 2: Will the radius of circle having area 676π square inches have length of radius less than 30 inches or more than 30 inches?

    Solution

    Radius can be found using the formula of area of a circle is πr2 square inches. By the given information,

    πr2 = 676π 
    r2 = 676

    By taking the square root on both sides we get, √r2= √676. We know that the square root of r2 is r. By calculating the square root of 676 is 26 inches. Hence, the radius of circle having area 676π square inches will have length of radius less than 30 inches.

Check Answer >

go to slidego to slide

 

Great learning in high school using simple cues
Indulging in rote learning, you are likely to forget concepts. With Cuemath, you will learn visually and be surprised by the outcomes.

Book a Free Trial Class

 

FAQs on Square Root of 676

What are the two square roots of 676?

The square roots of 676 are -26 and 26.

Is 676 a perfect square?

Yes, 676 is a perfect square.

Does 676 have a square root?

Yes, 676 has a square root. The √676 is 26.

Can square root of 676 simplified?

676 can be broken down as a product of 2 × 2 × 13 × 13. The square root of 676 gives output as 26.

Is the square root of 676 rational or irrational?

The square root of 676 is rational.

Is square root of 676 a real number?

Yes, the square root of 676 is a real number.

Math worksheets and
visual curriculum