Square Root of 182
The square root of 182 is expressed as √182 in the radical form and as (182)^{½} or (182)^{0.5} in the exponent form. The square root of 182 rounded up to 9 decimal places is 13.490737563. It is the positive solution of the equation x^{2} = 182.
 Square Root of 182: 13.490737563232042
 Square Root of 182 in exponential form: (182)^{½} or (182)^{0.5}
 Square Root of 182 in radical form: √182
1.  What is the Square Root of 182? 
2.  How to find the Square Root of 182? 
3.  Is the Square Root of 182 Irrational? 
4.  FAQs 
What is the Square Root of 182?
The square root of 182, (or root 182), is the number which when multiplied by itself gives the product as 182. Therefore, the square root of 182 = √182 = 13.490737563232042.
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How to Find Square Root of 182?
Value of √182 by Long Division Method
Explanation:
 Forming pairs: 01 and 82
 Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
 Bring down the next pair 82, to the right of the remainder 0. The new dividend is now 82.
 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 3) such that 2Z × Z <= 82. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 82.
 Divide 82 by 23 with the quotient as 3, giving the remainder = 82  23 × 3 = 82  69 = 13.
 Now, let's find the decimal places after the quotient 13.
 Bring down 00 to the right of this remainder 13. The new dividend is now 1300.
 Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 4) such that 26Z × Z <= 1300. Together they form a new divisor (264) for the new dividend (1300).
 Divide 1300 by 264 with the quotient as 4, giving the remainder = 1300  264 × 4 = 1300  1056 = 244.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 182.
Therefore, the square root of 182 by long division method is 13.4 approximately.
Is Square Root of 182 Irrational?
The actual value of √182 is undetermined. The value of √182 up to 25 decimal places is 13.49073756323204146555031. Hence, the square root of 182 is an irrational number.
ā Also Check:
 Square Root of 28  √28 = 5.29150
 Square Root of 225  √225 = 15
 Square Root of 108  √108 = 10.39230
 Square Root of 320  √320 = 17.88854
 Square Root of 105  √105 = 10.24695
 Square Root of 68  √68 = 8.24621
 Square Root of 10  √10 = 3.16228
Square Root of 182 Solved Examples

Example 1: Solve the equation x^{2} − 182 = 0
Solution:
x^{2}  182 = 0 i.e. x^{2} = 182
x = ±√182
Since the value of the square root of 182 is 13.491,
⇒ x = +√182 or √182 = 13.491 or 13.491. 
Example 2: If the area of an equilateral triangle is 182√3 in^{2}. Find the length of one of the sides of the triangle.
Solution:
Let 'a' be the length of one of the sides of the equilateral triangle.
⇒ Area of the equilateral triangle = (√3/4)a^{2} = 182√3 in^{2}
⇒ a = ±√728 in
Since length can't be negative,
⇒ a = √728 = 2 √182
We know that the square root of 182 is 13.491.
⇒ a = 26.981 in 
Example 3: If the surface area of a sphere is 728π in^{2}. Find the radius of the sphere.
Solution:
Let 'r' be the radius of the sphere.
⇒ Area of the sphere = 4πr^{2} = 728π in^{2}
⇒ r = ±√182 in
Since radius can't be negative,
⇒ r = √182
The square root of 182 is 13.491.
⇒ r = 13.491 in
FAQs on the Square Root of 182
What is the Value of the Square Root of 182?
The square root of 182 is 13.49073.
Why is the Square Root of 182 an Irrational Number?
Upon prime factorizing 182 i.e. 2^{1} × 7^{1} × 13^{1}, 2 is in odd power. Therefore, the square root of 182 is irrational.
Evaluate 9 plus 9 square root 182
The given expression is 9 + 9 √182. We know that the square root of 182 is 13.491. Therefore, 9 + 9 √182 = 9 + 9 × 13.491 = 9 + 121.417 = 130.417
If the Square Root of 182 is 13.491. Find the Value of the Square Root of 1.82.
Let us represent √1.82 in p/q form i.e. √(182/100) = 1.82/10 = 1.349. Hence, the value of √1.82 = 1.349
What is the Square of the Square Root of 182?
The square of the square root of 182 is the number 182 itself i.e. (√182)^{2} = (182)^{2/2} = 182.
Is the number 182 a Perfect Square?
The prime factorization of 182 = 2^{1} × 7^{1} × 13^{1}. Here, the prime factor 2 is not in the pair. Therefore, 182 is not a perfect square.