Square Root of 729
729 is a perfect square number which is obtained by square of 27. Hence, the square root of 729 is a rational number. Square root is described with the symbol √. If n is an integer, then square of n is equal to m which is also an integer. If n² = m, then n=√m. The square root of 729 is written as √729. Let us explore the square root of 729 in detail. 729 is a composite number, as it has more than 2 factors. In this minilesson we will learn to find square root of 729 along with solved examples. Let us see what the square root of 729 is.
 Square Root of 729: √729 = 27
 Square of 729: 729^{2} = 5,31,441
1.  What Is the Square Root of 729? 
2.  Is Square Root of 729 Rational or Irrational? 
3.  How to Find the Square Root of 729? 
4.  Important Notes 
5.  Thinking Out of the Box! 
6.  FAQs on Square Root of 729 
What Is the Square Root of 729?
The number whose square is 729 is the square root of 729.
√729 = 27
The answer which we get on squaring 27² is 729. This makes 729 a perfect square.
Is the Square Root of 729 Rational or Irrational?
A rational number can be either terminating or nonterminating and has a repeating pattern in its decimal part. We saw that √729 = 27. 27 is a whole number. It is possible to express it in p/q form easily. Hence, √729 is a rational number.
How to Find the Square Root of 729?
There are different methods to find the square root of any number. Click here to know more about it. The factors of 729 are 1, 3, 9, 27, 81, 243, and 729.
As 729 has more than 2 factors, it is a composite number
To find the square root of 729:
 We can use prime factorization method to obtain one number from each pair of the same numbers and multiply them. The prime factorization of 729 is 3 × 3 × 3 × 3 × 3 × 3 which consists of 3 pairs of the same number, 3 × 3 x 3. Thus, the square root of 729 = 9 × 3 = 27.
 Since 729 is a perfect square, we can also express it as 27^{2}. The number within square root which gets repeated is √(27 × 27) = 27. Hence, the square root of 729 is 27.
√729 = √27² = (27)^{2 × ½} = 27
The square root of 729 is 27.
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Important Notes:
 729 is a perfect square as the answer obtained after square root is a rational number.
 The square root of 729 can be simplified to 27 either by using the prime factorization of 729 or by expressing 729 as a square of 27.
Think Tank:
 Can the value of a square root of 729 be decimal?
 Is √729 a real number?
Square Root of 729 Solved Examples

Example 1: What is the difference in lengths of square boxes having area 729 square inches and 289 square inches ?
Solution
As the area of square box is area = length × length
The length of square box having area 289 square inches is √289 = 17 inches.
Similarly the length of box having area 729 square inches is √729 = 27 inches.
The difference in lengths of boxes is (27  17) inches = 10 inches
Hence, the difference in length of square boxes having area 729 square inches and 289 square inches is 10 inches. 
Example 2: Can you determine the radius of circle having area 729π square inches?
Solution
Radius can be found using the formula of area of a circle is πr^{2} square inches. By the given information,
πr^{2} = 729π
r^{2} = 729
By taking the square root on both sides we get, √r^{2}= √729. We know that the square root of r^{2} is r.
By calculating the square root of 729 is 27 inches. 
Example 3: Can you determine the square root of 729 using long division method?
Solution
To find the square root of 729 using long division method we need to follow the following steps:
Step 1. Write 729 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 29.
Step 2. Now find a number (n) such that n × n is a number less than equal to 7. Hence, n = 2 (2 × 2 = 4).
Step 3. 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 (29). The remiander is 329.
Step 4. Now find a number (m) such that 2m × m is less than equal to 329. Here m will be 7 as 47 × 7 = 329.
FAQs on Square Root of 729
What are the two square roots of 729?
The square roots of 729 are 27 and 27.
Is 729 a perfect square?
Yes, 729 is a perfect square.
Does 729 have a square root?
Yes, 729 has a square root.
Can square root of 729 be simplified?
729 can be broken down as a product of 27 × 27. Either ways, the square root of 729 gives output as 27.
Is the square root of 729 rational or irrational?
The square root of 729 is rational.
Is square root of 729 a real number?
Yes, the square root of 729 is a real number.
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