Which expression is equivalent to √184
The square root of 184 cannot be simplified exactly because 184 is not a perfect square. However, it can be approximated to a decimal number, or it can be expressed in terms of the square roots of its prime factors.
First, let's find the prime factorization of 184:
184 = 2 × 92
92 = 2 × 46
46 = 2 × 23
Since 23 is a prime number, the prime factorization of 184 is:
184 = 2 × 2 × 2 × 23
184 = 2^3 × 23
Now, we know that the square root of a product of factors is the product of the square roots of those factors, so:
√184 = √(2^3 × 23)
You can separate this into the square root of each prime factor raised to its power:
√184 = √(2^2) × √(2 × 23)
Since 2^2 is a perfect square (4), we know that √(2^2) = 2. We are left with:
√184 = 2 × √(2 × 23)
√184 = 2 × √46
As neither 2 nor 23 is a perfect square, this is about as simplified as you can make it without turning to a decimal approximation. If you were to approximate it to a decimal, you'd have:
√184 ≈ 13.5647 (rounded to four decimal places).