Square Root of 161
The square root of 161 is expressed as √161 in the radical form and as (161)^{½} or (161)^{0.5} in the exponent form. The square root of 161 rounded up to 6 decimal places is 12.688578. It is the positive solution of the equation x^{2} = 161.
 Square Root of 161: 12.68857754044952
 Square Root of 161 in exponential form: (161)^{½} or (161)^{0.5}
 Square Root of 161 in radical form: √161
1.  What Is the Square Root of 161? 
2.  Is Square Root of 161 Rational or Irrational? 
3.  How to Find the Square Root of 161? 
4.  Important Notes 
5.  FAQs on Square Root of 161 
What Is the Square Root of 161?
The square root of a number n is written as √n. This number when squared or multiplied by itself gives the original number n. The square root of 161 can be represented in multiple ways:
 Radical form: √161
 Decimal form: 12.688
 Exponent form: (161)^{1/2}
Is Square Root of 161 Rational or Irrational?
 161 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
 Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 161 is an irrational number.
How to Find the Square Root of 161?
There are 2 ways to find the square root of 161:
 Long Division Method
 Prime Factorization
One can find out other methods by clicking here.
Long Division Method
The square root of 161 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits of 161 by putting a bar above 61 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number which, when multiplied by itself, gives a product less than or equal to 1. This will be 1 obviously, so place 1 in the quotient and the divisor's place, which will result in the remainder being 0.
 Step 3: Drag down 61 beside the remainder 0. Also, add the divisor to itself and write it below. (1 + 1 = 2).
 Step 4: Find a number X such that 2X × X results in a number less than or equal to 61. The number 2 fits here so fill it next to 2 in the divisor as well as next to 1 in the quotient.
 Step 5: Find the remainder and now drag down the pair of 0s from the decimal part of the number. Adding X to the divisor, the new divisor becomes 24.
 Step 6: Repeat this process to get the decimal places you want.
Therefore, the square root of 161 = 12.688.
Estimation and Approximation
The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.
 First, we will find the two consecutive numbers such that 161 lies between their perfect squares. In this case, the numbers are 12 (144) and 13 (169). We take the whole number part to be the smaller perfect square, in this case, 12.
 Now, for the decimal part we will use the below formula: (Given number – Smaller perfect square) / (Greater perfect square – smaller perfect square)
= (161  144)/(169  144) = 17/25 = 0.68
Therefore, the square root of 161 ≅ 12.68.
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Important Notes
 There are positive and negative root of 161: 12.688 and 12.688.
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits.
Solved Examples

Example 1: Robert wants to cover his room's floor with tiles and needs to know the floor dimensions. The floor is squareshaped and it has an area of 161 square feet. What will be the length of the room's floor? Round your answer to the nearest tenth.
Solution:
Let us assume that the length of the room is x feet. Then the area of the room's floor is x^{2} square feet. By the given information:
x^{2} = 161
x = √161 = 12.688 feet
The final answer is rounded to the nearest tenth. Hence, the length of the room is 12.7 feet. 
Example 2: What is the circumference of a circular racing track having an area of 322π square inches?
Solution:
The area is found using the formula of the area of a circle, which is πr^{2}. By the given information,
πr^{2} = 322π
r^{2} = 161 × 2
r = √(2 × 12.688) = 17.944
Cirfumference = C = 2πr = 112.745
Therefore, the radius of the circle is ≅ 112.75 inches. 
Example: If the area of an equilateral triangle is 161√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} = 161√3 in^{2}
⇒ a = ±√644 in
Since length can't be negative,
⇒ a = √644 = 2 √161
We know that the square root of 161 is 12.689.
⇒ a = 25.377 in
FAQs on the Square Root of 161
What is the Value of the Square Root of 161?
The square root of 161 is 12.68857.
Why is the Square Root of 161 an Irrational Number?
Upon prime factorizing 161 i.e. 7^{1} × 23^{1}, 7 is in odd power. Therefore, the square root of 161 is irrational.
What is the Value of 15 square root 161?
The square root of 161 is 12.689. Therefore, 15 √161 = 15 × 12.689 = 190.329.
Evaluate 11 plus 3 square root 161
The given expression is 11 + 3 √161. We know that the square root of 161 is 12.689. Therefore, 11 + 3 √161 = 11 + 3 × 12.689 = 11 + 38.066 = 49.066
If the Square Root of 161 is 12.689. Find the Value of the Square Root of 1.61.
Let us represent √1.61 in p/q form i.e. √(161/100) = 1.61/10 = 1.269. Hence, the value of √1.61 = 1.269
Is the number 161 a Perfect Square?
The prime factorization of 161 = 7^{1} × 23^{1}. Here, the prime factor 7 is not in the pair. Therefore, 161 is not a perfect square.
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