Mistakes students make simplifying radicals

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Mathematics
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11th Grade - University
•
Hard
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7 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a common mistake students make when simplifying expressions like sqrt(25x^2)?
Ignoring the square root entirely
Adding the square root to the exponent
Distributing the square root over addition or subtraction
Multiplying the square root by 2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How should you simplify a perfect square trinomial like x^2 + 4x + 4?
By factoring it into a binomial squared
By distributing the square root
By adding the terms directly
By multiplying each term by 2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is a more efficient method for simplifying sqrt(48)?
Using prime factorization
Finding the largest square factor
Dividing by 2 repeatedly
Adding all factors together
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to find the largest square factor when simplifying radicals?
It makes the problem unsolvable
It reduces the number of steps needed
It increases the complexity of the problem
It ensures the answer is a whole number
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the rule for taking the square root of a negative number?
It is possible with any index
It is not possible with even indices
It is possible only with even indices
It is always possible
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can you simplify the cube root of a negative number?
By using the negative base raised to the power of three
By adding 1 to the number
By rewriting it as the cube root of a positive number
By ignoring the negative sign
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When is it necessary to use absolute values in radical expressions?
When the expression contains a variable
When the index is odd
When the index is even and the result is raised to an odd power
When the result is a negative number
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