Question

simplify \\(\sqrt{22}\\)

Explanation:

Step1: Factorize 22

To simplify $\sqrt{22}$, we first factorize 22. The prime factorization of 22 is $22 = 2\times11$.

Step2: Check for perfect squares

A square root can be simplified if there is a perfect square factor. But 2 and 11 are both prime numbers, and neither 2 nor 11 is a perfect square (since the square of an integer, e.g., $1^2 = 1$, $2^2 = 4$, $3^2 = 9$, etc., and 2 and 11 are not among these). So, we cannot simplify $\sqrt{22}$ further using the property $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ (where $a$ and $b$ are non - negative real numbers) to get a simpler radical form with integer factors. We can, however, find its approximate decimal value.

Step3: Calculate the approximate value (optional for simplification check)

Using a calculator, $\sqrt{22}\approx4.690$. But in terms of radical simplification, since 22 has no perfect square factors other than 1, $\sqrt{22}$ is already in its simplest radical form.

Answer:

$\sqrt{22}$ (or approximately $4.69$ if a decimal approximation is acceptable)