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Square Root of 164

The square root of 164 is expressed as √164 in the radical form and as (164)^½ or (164)^0.5 in the exponent form. The square root of 164 rounded up to 7 decimal places is 12.8062485. It is the positive solution of the equation x² = 164. We can express the square root of 164 in its lowest radical form as 2 √41.

Square Root of 164: 12.806248474865697
Square Root of 164 in exponential form: (164)^½ or (164)^0.5
Square Root of 164 in radical form: √164 or 2 √41

1.	What Is the Square Root of 164?
2.	Is Square Root of 164 Rational or Irrational?
3.	How to Find the Square Root of 164?
4.	FAQs on Square Root of 164

What Is the Square Root of 164?

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. The square root of 164 can be written in multiple ways:

Radical form: √164 = 2√41
Decimal form: 12.806
Exponent form: (164)^1/2

Is Square Root of 164 Rational or Irrational?

164 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 164 is an irrational number.

How to Find the Square Root of 164?

There are 2 ways to find the square root of 164:

Long Division Method
Prime Factorization

One can find out other methods by clicking here.

Long Division Method

The square root of 164 by long division method consists of the following steps:

Step 1: Starting from the right, we will pair up the digits of 164 by putting a bar above 64 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 64 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 64. 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 164 = 12.806

Prime Factorization

To find the square root of 164, we shall first express it in terms of its prime factors.
164 = 2 × 2 × 41
Next, this can be reduced further to
164 = 2² × 41
Finally, to find the root of this from here it is very easy,
√164 = √(2² × 41)
√164 = 2√41 = 12.806

Therefore, the square root of 164 ≅ 12.806

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Important Notes

There are positive and negative root of 164: 12.806 and -12.806
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.

Example 1: Mike wants to cover his room's floor with tiles and needs to know the floor dimensions. The floor is square-shaped and it has an area of 164 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 x² square feet. By the given information:
x² = 164
x = √164 = 12.806 feet
The final answer is rounded to the nearest tenth. Hence, the length of the room is 12.8 feet.
Example 2: What is the radius of a circular park having an area of 328π square feet?

Solution:

The area is found using the formula of the area of a circle, which is πr². By the given information,
πr² = 328π
r² = 164 × 2
r = √2 × 12.8 = 18.1
Therefore, the radius of the circle is ≅ 18 feet (approx.)
Example 3: If the area of an equilateral triangle is 164√3 in². 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)a² = 164√3 in²
⇒ a = ±√656 in
Since length can't be negative,
⇒ a = √656 = 2 √164
We know that the square root of 164 is 12.806.
⇒ a = 25.612 in

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FAQs on the Square Root of 164

What is the Value of the Square Root of 164?

The square root of 164 is 12.80624.

Why is the Square Root of 164 an Irrational Number?

Upon prime factorizing 164 i.e. 2² × 41¹, 41 is in odd power. Therefore, the square root of 164 is irrational.

If the Square Root of 164 is 12.806. Find the Value of the Square Root of 1.64.

Let us represent √1.64 in p/q form i.e. √(164/100) = 1.64/10 = 1.281. Hence, the value of √1.64 = 1.281

Evaluate 6 plus 6 square root 164

The given expression is 6 + 6 √164. We know that the square root of 164 is 12.806. Therefore, 6 + 6 √164 = 6 + 6 × 12.806 = 6 + 76.837 = 82.837

What is the Value of 9 square root 164?

The square root of 164 is 12.806. Therefore, 9 √164 = 9 × 12.806 = 115.256.

What is the Square of the Square Root of 164?

The square of the square root of 164 is the number 164 itself i.e. (√164)² = (164)^2/2 = 164.

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