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Square Root of 784

784 is a perfect square number which is obtained by square of 28. Hence, the square root of 784 is a rational number. Square root is described with the symbol √. If n is an integer, then the square of n is equal to m which is also an integer. If n² = m, then n=√m. The square root of 784 is written as √784. Let us explore the square root of 784 in detail. 784 is a composite number, as it has more than 2 factors. In this mini-lesson we will learn to find the square root of 784 along with solved examples. Let us see what the square root of 784 is.

  • Square Root of 784: √784 = 28
  • Square of 784: 7842 = 614656
1. What Is the Square Root of 784?
2. Is Square Root of 784 Rational or Irrational?
3. How to Find the Square Root of 784?
4. FAQs on Square Root of 784

What Is the Square Root of 784?

The original number whose square is 784 gives the square root of 784. (√784 = 28)
The answer which we get on squaring 28² is 784. This makes 784 a perfect square.

Is the Square Root of 784 Rational or Irrational?

A rational number can be either terminating or non-terminating and has a repeating pattern in its decimal part. We saw that √784 = 28. 28 is a whole number. It is possible to express it in p/q form easily. Hence, √784 is a rational number.

How to Find the Square Root of 784?

There are different methods to find the square root of any number. Click here to know more about it.
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, and 784.
As 784 has more than 2 factors, it is a composite number

To find the square root of 784:

  • We can use prime factorization method to obtain one number from each pair of the same numbers and multiply them. The prime factorization of 784 is 2 × 2 × 2 × 2 × 7 × 7 which consists of 3 pairs of the same numbers 2 and 7. Thus, the square root of 784 = 4 × 7 = 28.

Square Root of 784 Using Prime Factorization

  • Since 784 is a perfect square, we can also express it as 282. The number within square root which gets repeated is √(28 × 28) = 28. Hence, the square root of 784 is 28.
    √784 = √28² = (28)2 × ½ = 28

The square root of 784 is 28.

Explore square roots using illustrations and interactive examples

Important Notes:

  • 784 is a perfect square as the answer obtained after square root is a rational number.
  • The square root of 784 can be simplified to 28 either by using the prime factorization of 784 or by expressing 784 as a square of 28.

Think Tank:

  • Can the value of a square root of 784 be decimal?
  • Is √-784 a real number? 
 

Square Root of 784 Solved Examples

  1. Example 1: What is the difference in lengths of square boxes having area 784 square inches and 729 square inches?

    Solution

    Area of the square box is length × length
    The length of square box having area 784 square inches is √784 = 28 inches. 
    Similarly, the length of box having area 729 square inches is √729 = 27 inches.
    The difference in lengths of boxes is (28 - 27) inches = 1 inch
    Hence, the difference in length of square boxes having area 784 square inches and 729 square inches is 1 inch.

  2. Example 2: Can you determine the radius of circle having area 784π square inches?

    Solution

    Radius can be found using the formula of area of a circle as πr2 square inches. By the given information,
    πr2 = 784π 
    r2 = 784
    By taking the square root on both sides, we get √r2= √784. We know that the square root of r2 is r.
    On calculating the square root of 784, the radius of the circle comes as 28 inches.

  3. Example 3: Can you determine the square root of 784 using long division method?

    Solution

    To find the square root of 784 using long division method, we need to follow the steps:
    Step1. Write 784 as shown in the figure. Start pairing the digits from the right end in pairs of two by putting a bar on top of them. So, we got two pairs of 7 and 84
    Step2. Now find a number (n) such that n × n is a number less than equal to 7. Hence, n = 2 (2 × 2 = 4).
    Step3. Now subtract the obtained value from the first pair in the dividend and add the divisor with itself (n + n) (2 + 2 = 4). Now bring the second pair down (84).
    Step4. The new dividend is 384. Double the quotient to get the first digit of the new divisor. The digit in the tens place will be 4.
    Step5. Find the digit at the units place of divisor such that when it gives number less than equal to 384.
    Step6. The number is 8. Now we get our new divisor as 48. 48 × 8 = 384. Complete the division and get the remainder. We finally get 0. Thus, the process of division completes here.
    Square root of 784 by long division method is 28.

    Square Root of 784

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FAQs on Square Root of 784

What are the two square roots of 784?

The square roots of 784 are -28 and 28.

Is 784 a perfect square?

Yes, 784 is a perfect square

Does 784 have a square root?

Yes, 784 has a square root.

Can square root of 784 be simplified?

784 can be broken down as a product of 28 × 28. Either ways, the square root of 784 gives output as 28.

Is the square root of 784 rational or irrational?

The square root of 784 is rational.

Is square root of 784 a real number?

Yes, the square root of 784 is a real number.

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