Square Root of 968
The square root of 968 is expressed as √968 in the radical form and as (968)^{½} or (968)^{0.5} in the exponent form. The square root of 968 rounded up to 9 decimal places is 31.112698372. It is the positive solution of the equation x^{2} = 968. We can express the square root of 968 in its lowest radical form as 22 √2.
 Square Root of 968: 31.11269837220809
 Square Root of 968 in exponential form: (968)^{½} or (968)^{0.5}
 Square Root of 968 in radical form: √968 or 22 √2
1.  What is the Square Root of 968? 
2.  How to find the Square Root of 968? 
3.  Is the Square Root of 968 Irrational? 
4.  FAQs 
What is the Square Root of 968?
The square root of 968, (or root 968), is the number which when multiplied by itself gives the product as 968. Therefore, the square root of 968 = √968 = 22 √2 = 31.11269837220809.
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How to Find Square Root of 968?
Value of √968 by Long Division Method
Explanation:
 Forming pairs: 09 and 68
 Find a number Y (3) such that whose square is <= 9. Now divide 09 by 3 with quotient as 3.
 Bring down the next pair 68, to the right of the remainder 0. The new dividend is now 68.
 Add the last digit of the quotient (3) to the divisor (3) i.e. 3 + 3 = 6. To the right of 6, find a digit Z (which is 1) such that 6Z × Z <= 68. After finding Z, together 6 and Z (1) form a new divisor 61 for the new dividend 68.
 Divide 68 by 61 with the quotient as 1, giving the remainder = 68  61 × 1 = 68  61 = 7.
 Now, let's find the decimal places after the quotient 31.
 Bring down 00 to the right of this remainder 7. The new dividend is now 700.
 Add the last digit of quotient to divisor i.e. 1 + 61 = 62. To the right of 62, find a digit Z (which is 1) such that 62Z × Z <= 700. Together they form a new divisor (621) for the new dividend (700).
 Divide 700 by 621 with the quotient as 1, giving the remainder = 700  621 × 1 = 700  621 = 79.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 968.
Therefore, the square root of 968 by long division method is 31.1 approx.
Is Square Root of 968 Irrational?
The actual value of √968 is undetermined. The value of √968 up to 25 decimal places is 31.11269837220809107363715. Hence, the square root of 968 is an irrational number.
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Square Root of 968 Solved Examples

Example 1: Solve the equation x^{2} − 968 = 0
Solution:
x^{2}  968 = 0 i.e. x^{2} = 968
x = ±√968
Since the value of the square root of 968 is 31.113,
⇒ x = +√968 or √968 = 31.113 or 31.113. 
Example 2: If the surface area of a sphere is 3872π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 3872π in^{2}
⇒ r = ±√968 in
Since radius can't be negative,
⇒ r = √968
The square root of 968 is 31.113.
⇒ r = 31.113 in 
Example 3: If the area of a square is 968 in^{2}. Find the length of the side of the square.
Solution:
Let 'a' be the length of the side of the square.
⇒ Area of the square = a^{2} = 968 in^{2}
⇒ a = ±√968 in
Since length can't be negative,
⇒ a = √968 = 31.113 in
FAQs on the Square Root of 968
What is the Value of the Square Root of 968?
The square root of 968 is 31.11269.
Why is the Square Root of 968 an Irrational Number?
Upon prime factorizing 968 i.e. 2^{3} × 11^{2}, 2 is in odd power. Therefore, the square root of 968 is irrational.
What is the Square Root of 968 in Simplest Radical Form?
We need to express 968 as the product of its prime factors i.e. 968 = 2 × 2 × 2 × 11 × 11. Therefore, √968 = √2 × 2 × 2 × 11 × 11 = 22 √2. Thus, the square root of 968 in the lowest radical form is 22 √2.
Evaluate 5 plus 2 square root 968
The given expression is 5 + 2 √968. We know that the square root of 968 is 31.113. Therefore, 5 + 2 √968 = 5 + 2 × 31.113 = 5 + 62.225 = 67.225
What is the Value of 19 square root 968?
The square root of 968 is 31.113. Therefore, 19 √968 = 19 × 31.113 = 591.141.
Is the number 968 a Perfect Square?
The prime factorization of 968 = 2^{3} × 11^{2}. Here, the prime factor 2 is not in the pair. Therefore, 968 is not a perfect square.