Square Root of 276
The square root of 276 is expressed as √276 in the radical form and as (276)^{½} or (276)^{0.5} in the exponent form. The square root of 276 rounded up to 10 decimal places is 16.6132477258. It is the positive solution of the equation x^{2} = 276. We can express the square root of 276 in its lowest radical form as 2 √69.
 Square Root of 276: 16.61324772583615
 Square Root of 276 in exponential form: (276)^{½} or (276)^{0.5}
 Square Root of 276 in radical form: √276 or 2 √69
1.  What is the Square Root of 276? 
2.  How to find the Square Root of 276? 
3.  Is the Square Root of 276 Irrational? 
4.  FAQs 
What is the Square Root of 276?
The square root of 276, (or root 276), is the number which when multiplied by itself gives the product as 276. Therefore, the square root of 276 = √276 = 2 √69 = 16.61324772583615.
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How to Find Square Root of 276?
Value of √276 by Long Division Method
Explanation:
 Forming pairs: 02 and 76
 Find a number Y (1) such that whose square is <= 2. Now divide 02 by 1 with quotient as 1.
 Bring down the next pair 76, to the right of the remainder 1. The new dividend is now 176.
 Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 6) such that 2Z × Z <= 176. After finding Z, together 2 and Z (6) form a new divisor 26 for the new dividend 176.
 Divide 176 by 26 with the quotient as 6, giving the remainder = 176  26 × 6 = 176  156 = 20.
 Now, let's find the decimal places after the quotient 16.
 Bring down 00 to the right of this remainder 20. The new dividend is now 2000.
 Add the last digit of quotient to divisor i.e. 6 + 26 = 32. To the right of 32, find a digit Z (which is 6) such that 32Z × Z <= 2000. Together they form a new divisor (326) for the new dividend (2000).
 Divide 2000 by 326 with the quotient as 6, giving the remainder = 2000  326 × 6 = 2000  1956 = 44.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 276.
Therefore, the square root of 276 by long division method is 16.6 approx.
Is Square Root of 276 Irrational?
The actual value of √276 is undetermined. The value of √276 up to 25 decimal places is 16.61324772583614970516853. Hence, the square root of 276 is an irrational number.
☛ Also Check:
 Square Root of 50  √50 = 7.07107
 Square Root of 44  √44 = 6.63325
 Square Root of 68  √68 = 8.24621
 Square Root of 29  √29 = 5.38516
 Square Root of 512  √512 = 22.62742
 Square Root of 676  √676 = 26
 Square Root of 1681  √1681 = 41
Square Root of 276 Solved Examples

Example 1: Solve the equation x^{2} − 276 = 0
Solution:
x^{2}  276 = 0 i.e. x^{2} = 276
x = ±√276
Since the value of the square root of 276 is 16.613,
⇒ x = +√276 or √276 = 16.613 or 16.613. 
Example 2: If the area of a circle is 276π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 276π in^{2}
⇒ r = ±√276 in
Since radius can't be negative,
⇒ r = √276
The square root of 276 is 16.613.
⇒ r = 16.613 in 
Example 3: If the surface area of a cube is 1656 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} = 1656 in^{2}
⇒ a = ±√276 in
Since length can't be negative,
⇒ a = √276
We know that the square root of 276 is 16.613.
⇒ a = 16.613 in
FAQs on the Square Root of 276
What is the Value of the Square Root of 276?
The square root of 276 is 16.61324.
Why is the Square Root of 276 an Irrational Number?
Upon prime factorizing 276 i.e. 2^{2} × 3^{1} × 23^{1}, 3 is in odd power. Therefore, the square root of 276 is irrational.
What is the Square Root of 276?
The square root of 276 is an imaginary number. It can be written as √276 = √1 × √276 = i √276 = 16.613i
where i = √1 and it is called the imaginary unit.
What is the Square of the Square Root of 276?
The square of the square root of 276 is the number 276 itself i.e. (√276)^{2} = (276)^{2/2} = 276.
Evaluate 13 plus 17 square root 276
The given expression is 13 + 17 √276. We know that the square root of 276 is 16.613. Therefore, 13 + 17 √276 = 13 + 17 × 16.613 = 13 + 282.425 = 295.425
What is the Value of 9 square root 276?
The square root of 276 is 16.613. Therefore, 9 √276 = 9 × 16.613 = 149.519.