A day full of math games & activities. Find one near you.

Square Root of 184

The square root of 184 is expressed as √184 in the radical form and as (184)^½ or (184)^0.5 in the exponent form. The square root of 184 rounded up to 5 decimal places is 13.56466. It is the positive solution of the equation x² = 184. We can express the square root of 184 in its lowest radical form as 2 √46.

Square Root of 184: 13.564659966250536
Square Root of 184 in exponential form: (184)^½ or (184)^0.5
Square Root of 184 in radical form: √184 or 2 √46

Square Root of 184

1.	What is the Square Root of 184?
2.	How to find the Square Root of 184?
3.	Is the Square Root of 184 Irrational?
4.	FAQs

What is the Square Root of 184?

The square root of 184, (or root 184), is the number which when multiplied by itself gives the product as 184. Therefore, the square root of 184 = √184 = 2 √46 = 13.564659966250536.

☛ Check: Square Root Calculator

How to Find Square Root of 184?

Square Root of 184 by Long Division Method

Value of √184 by Long Division Method

Explanation:

Forming pairs: 01 and 84
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 84, to the right of the remainder 0. The new dividend is now 84.
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 <= 84. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 84.
Divide 84 by 23 with the quotient as 3, giving the remainder = 84 - 23 × 3 = 84 - 69 = 15.
Now, let's find the decimal places after the quotient 13.
Bring down 00 to the right of this remainder 15. The new dividend is now 1500.
Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 5) such that 26Z × Z <= 1500. Together they form a new divisor (265) for the new dividend (1500).
Divide 1500 by 265 with the quotient as 5, giving the remainder = 1500 - 265 × 5 = 1500 - 1325 = 175.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 184.

Therefore, the square root of 184 by long division method is 13.5 approx.

Is Square Root of 184 Irrational?

The actual value of √184 is undetermined. The value of √184 up to 25 decimal places is 13.56465996625053627812911. Hence, the square root of 184 is an irrational number.

☛ Also Check:

Square Root of 1521 - √1521 = 39
Square Root of 80 - √80 = 8.94427
Square Root of 39 - √39 = 6.24500
Square Root of 8 - √8 = 2.82843
Square Root of 52 - √52 = 7.21110
Square Root of 240 - √240 = 15.49193
Square Root of 120 - √120 = 10.95445

Square Root of 184 Solved Examples

Example 1: Solve the equation x² − 184 = 0

Solution:

x² - 184 = 0 i.e. x² = 184
x = ±√184
Since the value of the square root of 184 is 13.565,
⇒ x = +√184 or -√184 = 13.565 or -13.565.
Example 2: If the area of a circle is 184π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 184π in²
⇒ r = ±√184 in
Since radius can't be negative,
⇒ r = √184
The square root of 184 is 13.565.
⇒ r = 13.565 in
Example 3: If the surface area of a cube is 1104 in². 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 = 6a² = 1104 in²
⇒ a = ±√184 in
Since length can't be negative,
⇒ a = √184
We know that the square root of 184 is 13.565.
⇒ a = 13.565 in

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on the Square Root of 184

What is the Value of the Square Root of 184?

The square root of 184 is 13.56465.

Why is the Square Root of 184 an Irrational Number?

Upon prime factorizing 184 i.e. 2³ × 23¹, 2 is in odd power. Therefore, the square root of 184 is irrational.

What is the Square of the Square Root of 184?

The square of the square root of 184 is the number 184 itself i.e. (√184)² = (184)^2/2 = 184.

Is the number 184 a Perfect Square?

The prime factorization of 184 = 2³ × 23¹. Here, the prime factor 2 is not in the pair. Therefore, 184 is not a perfect square.

What is the Square Root of 184 in Simplest Radical Form?

We need to express 184 as the product of its prime factors i.e. 184 = 2 × 2 × 2 × 23. Therefore, √184 = √2 × 2 × 2 × 23 = 2 √46. Thus, the square root of 184 in the lowest radical form is 2 √46.

What is the Value of 17 square root 184?

The square root of 184 is 13.565. Therefore, 17 √184 = 17 × 13.565 = 230.599.

Math worksheets and
visual curriculum