Square Root of 160
The square root of 160 is expressed as √160 in the radical form and as (160)^{½} or (160)^{0.5} in the exponent form. The square root of 160 rounded up to 7 decimal places is 12.6491106. It is the positive solution of the equation x^{2} = 160. We can express the square root of 160 in its lowest radical form as 4 √10.
 Square Root of 160: 12.649110640673518
 Square Root of 160 in exponential form: (160)^{½} or (160)^{0.5}
 Square Root of 160 in radical form: √160 or 4 √10
1.  What Is the Square Root of 160? 
2.  Is Square Root of 160 Rational or Irrational? 
3.  How to Find the Square Root of 160? 
4.  Challenging Questions 
5.  FAQs on Square Root of 160 
What Is the Square Root of 160?
The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. There are multiple ways of writing square root of 160. They are given as:
 Radical form: √160 = 4√10
 Decimal form: 12.649
 Exponent form: (160)^{1/2}
Is Square Root of 160 Rational or Irrational?
 160 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 160 is an irrational number.
How to Find the Square Root of 160?
There are only 2 ways to find the square root of 160:
 Long Division Method
 Prime Factorization
We cannot use the prime factorization method here, as 160 is a prime number. Think about it?
Long Division Method
The square root of 160 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits 160 by putting a bar above 60 and 1 separately. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 160. The number 12 fits here as 12 squared gives 144. Dividing 160 by 12 with quotient as 12, we get the remainder as 16.
 Step 3: Drag a pair of 0’s down and fill it next to to make the dividend 1600.
 Step 4: Double the divisor 12, and enter 24 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 24X and X results in a value less than or equal to 1600. Since 6 fits the value of X, we fill 6 in the quotient after the decimal point. Divide and write the remainder.
 Step 5: Repeat this process to get the decimal places you want.
Therefore, the square root of 160 = 12.649
Prime Factorization
 To find the square root of 160, we shall first express it in terms of its prime factors. It can be expressed as 160 = 2 × 2 × 2 × 2 × 2 × 5.
 Next, this can be reduced further to 150 = 2^{5} × 5
 Finally, to find the root of this from here is very easy,
√150 = √(2^{5} × 5) = 4√(2 × 5) = 4√10 = 4 × 3.162 = 12.649
Therefore, the Square Root of 160 ≅ 12.649
Explore Square roots using illustrations and interactive examples
Challenging Questions
 What is the negative root of 160?
 Find the third root of 160?
 Express the below given numbers in the terms of square root of 160:
 256
 44100
Solved Examples

Example 1: Robert wants to buy a new painting for his living room. In the store, he finds a square painting that has an area of 16000 sq cm. How long is each side of the painting?
Solution:
To find the side of the painting, we will have to find the square root of 160.
The square root is √16000= 126.49.
Hence, the side length of the painting is 126.49 cm. 
Example 2: Find the square root of 25600 using the fact that square root of √160 =4√10.
Solution:
25600 = 160 × 160
√25600 = √(160 × 160) = (4√10 × 4√10)
√25600 = 160
Therefore, square root of 25600 is 160. 
Example: If the area of a circle is 160π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 160π in^{2}
⇒ r = ±√160 in
Since radius can't be negative,
⇒ r = √160
The square root of 160 is 12.649.
⇒ r = 12.649 in
FAQs on the Square Root of 160
What is the Value of the Square Root of 160?
The square root of 160 is 12.64911.
Why is the Square Root of 160 an Irrational Number?
Upon prime factorizing 160 i.e. 2^{5} × 5^{1}, 2 is in odd power. Therefore, the square root of 160 is irrational.
What is the Square Root of 160?
The square root of 160 is an imaginary number. It can be written as √160 = √1 × √160 = i √160 = 12.649i
where i = √1 and it is called the imaginary unit.
Is the number 160 a Perfect Square?
The prime factorization of 160 = 2^{5} × 5^{1}. Here, the prime factor 2 is not in the pair. Therefore, 160 is not a perfect square.
What is the Value of 15 square root 160?
The square root of 160 is 12.649. Therefore, 15 √160 = 15 × 12.649 = 189.737.
What is the Square of the Square Root of 160?
The square of the square root of 160 is the number 160 itself i.e. (√160)^{2} = (160)^{2/2} = 160.
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