each student will create an adding, subtracting, multiplying, or dividing expression containing square roots.you will simplify the expression and display it step by step. There can be no use of perfect squares in the original expression.
We are not the student. Good luck in creating.
Sure! Let's start by creating an example expression using square roots. Let's say a student has the expression:
√(5) + √(12) - √(2)
To simplify this expression, we need to apply the rules of adding, subtracting, multiplying, and dividing square roots. Let's break it down step by step:
Step 1: Simplify each square root separately.
√(5) can't be simplified any further because 5 is not a perfect square.
However, √(12) can be simplified by finding its perfect square factors. We can rewrite 12 as 4 * 3, and since 4 is a perfect square (2 * 2 = 4), we can simplify it as:
√(12) = √(4 * 3) = √(4) * √(3) = 2√(3)
Similarly, √(2) can't be simplified any further because 2 is not a perfect square.
Step 2: Re-write the expression with simplified square roots.
The expression becomes:
√(5) + 2√(3) - √(2)
Step 3: Collect like terms.
In this case, the like terms are the square roots:
(√(5) - √(2)) + 2√(3)
Step 4: Combine like terms.
The final simplified expression is:
(√(5) - √(2)) + 2√(3)
And that's how you simplify a given expression containing square roots step by step. You can now follow these steps to simplify other similar expressions created by different students.