Final answer:
Combining and simplifying radicals involve factoring out squares, simplifying the square roots, and combining like terms. It is also essential to eliminate superfluous terms and check the answer for reasonableness, ensuring the denominator is simplified as much as possible.
Step-by-step explanation:
To combine and simplify radicals, you need to follow a series of steps that include identifying like radicals and combining them, simplifying the expression within the radical as much as possible, and if needed, rationalizing the denominator. The typo in the original question makes identifying the exact radicals difficult, but assuming we are working with square roots, the steps would involve factoring out squares from the numbers within square roots, simplifying these factors, and then combining like terms. For example, for a square root like √8, we know that 8 is 2² × 2, so √8 simplifies to 2√2.
It's also essential to eliminate terms wherever possible to reduce the algebra to its simplest form. After simplifying, it is always a good practice to check the answer to ensure it's reasonable. Operations such as taking square roots of exponentials must consider the reduction of the exponential term for it to be evenly divisible by 2.
When dealing with an expression like √x², it's crucial to understand that this can be expressed as x to the power of 1/2. Simplifying the denominator, when possible, by writing it as a perfect square, can also help in simplifying the whole expression.