Square Root of 171
The square root of 171 is expressed as √171 in the radical form and as (171)^{½} or (171)^{0.5} in the exponent form. The square root of 171 rounded up to 5 decimal places is 13.07670. It is the positive solution of the equation x^{2} = 171. We can express the square root of 171 in its lowest radical form as 3 √19.
 Square Root of 171: 13.076696830622021
 Square Root of 171 in exponential form: (171)^{½} or (171)^{0.5}
 Square Root of 171 in radical form: √171 or 3 √19
1.  What is the Square Root of 171? 
2.  How to find the Square Root of 171? 
3.  Is the Square Root of 171 Irrational? 
4.  FAQs 
What is the Square Root of 171?
The square root of 171, (or root 171), is the number which when multiplied by itself gives the product as 171. Therefore, the square root of 171 = √171 = 3 √19 = 13.076696830622021.
☛ Check: Square Root Calculator
How to Find Square Root of 171?
Value of √171 by Long Division Method
Explanation:
 Forming pairs: 01 and 71
 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 71, to the right of the remainder 0. The new dividend is now 71.
 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 <= 71. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 71.
 Divide 71 by 23 with the quotient as 3, giving the remainder = 71  23 × 3 = 71  69 = 2.
 Now, let's find the decimal places after the quotient 13.
 Bring down 00 to the right of this remainder 2. The new dividend is now 200.
 Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 0) such that 26Z × Z <= 200. Together they form a new divisor (260) for the new dividend (200).
 Divide 200 by 260 with the quotient as 0, giving the remainder = 200  260 × 0 = 200  0 = 200.
 Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 171.
Therefore, the square root of 171 by long division method is 13.0 approx.
Is Square Root of 171 Irrational?
The actual value of √171 is undetermined. The value of √171 up to 25 decimal places is 13.07669683062202065671095. Hence, the square root of 171 is an irrational number.
☛ Also Check:
 Square Root of 320  √320 = 17.88854
 Square Root of 73  √73 = 8.54400
 Square Root of 192  √192 = 13.85641
 Square Root of 41  √41 = 6.40312
 Square Root of 325  √325 = 18.02776
 Square Root of 77  √77 = 8.77496
 Square Root of 40  √40 = 6.32456
Square Root of 171 Solved Examples

Example 1: Solve the equation x^{2} − 171 = 0
Solution:
x^{2}  171 = 0 i.e. x^{2} = 171
x = ±√171
Since the value of the square root of 171 is 13.077,
⇒ x = +√171 or √171 = 13.077 or 13.077. 
Example 2: If the area of a circle is 171π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 171π in^{2}
⇒ r = ±√171 in
Since radius can't be negative,
⇒ r = √171
The square root of 171 is 13.077.
⇒ r = 13.077 in 
Example 3: If the surface area of a cube is 1026 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} = 1026 in^{2}
⇒ a = ±√171 in
Since length can't be negative,
⇒ a = √171
We know that the square root of 171 is 13.077.
⇒ a = 13.077 in
FAQs on the Square Root of 171
What is the Value of the Square Root of 171?
The square root of 171 is 13.07669.
Why is the Square Root of 171 an Irrational Number?
Upon prime factorizing 171 i.e. 3^{2} × 19^{1}, 19 is in odd power. Therefore, the square root of 171 is irrational.
What is the Square of the Square Root of 171?
The square of the square root of 171 is the number 171 itself i.e. (√171)^{2} = (171)^{2/2} = 171.
What is the Square Root of 171 in Simplest Radical Form?
We need to express 171 as the product of its prime factors i.e. 171 = 3 × 3 × 19. Therefore, √171 = √3 × 3 × 19 = 3 √19. Thus, the square root of 171 in the lowest radical form is 3 √19.
Is the number 171 a Perfect Square?
The prime factorization of 171 = 3^{2} × 19^{1}. Here, the prime factor 19 is not in the pair. Therefore, 171 is not a perfect square.
What is the Value of 6 square root 171?
The square root of 171 is 13.077. Therefore, 6 √171 = 6 × 13.077 = 78.460.