Answer:

If n is a positive integer greater than 1 and both a and b are positive real numbers then,

1. Inverse Property

n√ an = a if n is odd or

n√ an = | a | if n is even

2. Product Rule n√ ab = n√ a · n√ b

3. Quotient Rule quotient rule

Note that on occasion we can allow a or b to be negative and still have theseproblem like √24 may look difficult because there is no number that we can multiply by itself to give 24. However, the problem can be simplified. So even though 24 is not a perfect square, it can be broken down into smaller pieces where one of those pieces might be a perfect square. So now we have √24 = √ 4 × 6 = √ 4 · √ 6 = 2√ 6 .

The following rules are very helpful in simplifying radicals.The square root of a number is always positive.

The number inside the radical sign is called the radicand. The entire expression is called a radical.

Example 1. Find the square root.

square root of 36 over 25

Solution.

answer 6 over 5

Use Product and Quotient Rules for Radicals

research one field of study that may involve the use of radical expressions give one specific example on how radical expression is used and copy the given example presented write your answer on the answer sheet provided