Square Root of 756
The square root of 756 is expressed as √756 in the radical form and as (756)^{½} or (756)^{0.5} in the exponent form. The square root of 756 rounded up to 8 decimal places is 27.49545417. It is the positive solution of the equation x^{2} = 756. We can express the square root of 756 in its lowest radical form as 6 √21.
 Square Root of 756: 27.49545416973504
 Square Root of 756 in exponential form: (756)^{½} or (756)^{0.5}
 Square Root of 756 in radical form: √756 or 6 √21
1.  What is the Square Root of 756? 
2.  How to find the Square Root of 756? 
3.  Is the Square Root of 756 Irrational? 
4.  FAQs 
What is the Square Root of 756?
The square root of 756, (or root 756), is the number which when multiplied by itself gives the product as 756. Therefore, the square root of 756 = √756 = 6 √21 = 27.49545416973504.
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How to Find Square Root of 756?
Value of √756 by Long Division Method
Explanation:
 Forming pairs: 07 and 56
 Find a number Y (2) such that whose square is <= 7. Now divide 07 by 2 with quotient as 2.
 Bring down the next pair 56, to the right of the remainder 3. The new dividend is now 356.
 Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 7) such that 4Z × Z <= 356. After finding Z, together 4 and Z (7) form a new divisor 47 for the new dividend 356.
 Divide 356 by 47 with the quotient as 7, giving the remainder = 356  47 × 7 = 356  329 = 27.
 Now, let's find the decimal places after the quotient 27.
 Bring down 00 to the right of this remainder 27. The new dividend is now 2700.
 Add the last digit of quotient to divisor i.e. 7 + 47 = 54. To the right of 54, find a digit Z (which is 4) such that 54Z × Z <= 2700. Together they form a new divisor (544) for the new dividend (2700).
 Divide 2700 by 544 with the quotient as 4, giving the remainder = 2700  544 × 4 = 2700  2176 = 524.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 756.
Therefore, the square root of 756 by long division method is 27.4 approximately.
Is Square Root of 756 Irrational?
The actual value of √756 is undetermined. The value of √756 up to 25 decimal places is 27.49545416973504003952828. Hence, the square root of 756 is an irrational number.
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Square Root of 756 Solved Examples

Example 1: Solve the equation x^{2} − 756 = 0
Solution:
x^{2}  756 = 0 i.e. x^{2} = 756
x = ±√756
Since the value of the square root of 756 is 27.495,
⇒ x = +√756 or √756 = 27.495 or 27.495. 
Example 2: If the surface area of a cube is 4536 in^{2}. Find the length of the side of the cube.
Solution:
Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a^{2} = 4536 in^{2}
⇒ a = ±√756 in
Since length can't be negative,
⇒ a = √756
We know that the square root of 756 is 27.495.
⇒ a = 27.495 in 
Example 3: If the area of a circle is 756π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 756π in^{2}
⇒ r = ±√756 in
Since radius can't be negative,
⇒ r = √756
The square root of 756 is 27.495.
⇒ r = 27.495 in
FAQs on the Square Root of 756
What is the Value of the Square Root of 756?
The square root of 756 is 27.49545.
Why is the Square Root of 756 an Irrational Number?
Upon prime factorizing 756 i.e. 2^{2} × 3^{3} × 7^{1}, 3 is in odd power. Therefore, the square root of 756 is irrational.
What is the Square Root of 756?
The square root of 756 is an imaginary number. It can be written as √756 = √1 × √756 = i √756 = 27.495i
where i = √1 and it is called the imaginary unit.
What is the Square Root of 756 in Simplest Radical Form?
We need to express 756 as the product of its prime factors i.e. 756 = 2 × 2 × 3 × 3 × 3 × 7. Therefore, √756 = √2 × 2 × 3 × 3 × 3 × 7 = 6 √21. Thus, the square root of 756 in the lowest radical form is 6 √21.
If the Square Root of 756 is 27.495. Find the Value of the Square Root of 7.56.
Let us represent √7.56 in p/q form i.e. √(756/100) = 7.56/10 = 2.750. Hence, the value of √7.56 = 2.750
Is the number 756 a Perfect Square?
The prime factorization of 756 = 2^{2} × 3^{3} × 7^{1}. Here, the prime factor 3 is not in the pair. Therefore, 756 is not a perfect square.