Question
Sandra was simplifying 4√√5. 2√3, and she ended up with 8√15 as her
simplified answer.
Is Sandra correct? If she is not correct, what was her mistake?
(1 point)
a. Sandra's simplified answer is correct.
b. Sandra's answer is not correct. She could continue to simplify the radical to get
24√5.
c.Sandra's answer is not correct. She should have added the coefficients to get
6√15
d. Sandra's answer is not correct. She should have multiplied 4 times 5 in the first
radical and multiplied 2 times 3 in the second radical to get a final answer of 26.
simplified answer.
Is Sandra correct? If she is not correct, what was her mistake?
(1 point)
a. Sandra's simplified answer is correct.
b. Sandra's answer is not correct. She could continue to simplify the radical to get
24√5.
c.Sandra's answer is not correct. She should have added the coefficients to get
6√15
d. Sandra's answer is not correct. She should have multiplied 4 times 5 in the first
radical and multiplied 2 times 3 in the second radical to get a final answer of 26.
Answers
Answered by
GPT-4o mini
To determine whether Sandra's answer of \( 8\sqrt{15} \) is correct for the expression \( 4\sqrt{5} + 2\sqrt{3} \), let's break down the problem step by step.
First, we see that the expression given is \( 4\sqrt{5} + 2\sqrt{3} \).
1. **Understanding radicals**:
- \( 4\sqrt{5} \) can't combine with \( 2\sqrt{3} \) because they are not the same radical (the numbers under the square root are different: 5 and 3).
2. **Combining terms**:
- Since you can't combine different radicals directly, you can only add or subtract coefficients of like terms.
3. **Final expression**:
- Therefore, you have \( 4\sqrt{5} \) and \( 2\sqrt{3} \). Since there are no like terms, you simply write the expression as it is:
\[
4\sqrt{5} + 2\sqrt{3}
\]
- This cannot be simplified to a single term.
Now, considering Sandra’s answer of \( 8\sqrt{15} \):
- She incorrectly combined the coefficients of \( 4\sqrt{5} \) and \( 2\sqrt{3} \) as if they were like terms which isn’t allowed since \( \sqrt{5} \) and \( \sqrt{3} \) are different.
Hence, the correct answer is:
**c. Sandra's answer is not correct. She should have added the coefficients to get \( 4\sqrt{5} + 2\sqrt{3} \), which does not simplify further.**
First, we see that the expression given is \( 4\sqrt{5} + 2\sqrt{3} \).
1. **Understanding radicals**:
- \( 4\sqrt{5} \) can't combine with \( 2\sqrt{3} \) because they are not the same radical (the numbers under the square root are different: 5 and 3).
2. **Combining terms**:
- Since you can't combine different radicals directly, you can only add or subtract coefficients of like terms.
3. **Final expression**:
- Therefore, you have \( 4\sqrt{5} \) and \( 2\sqrt{3} \). Since there are no like terms, you simply write the expression as it is:
\[
4\sqrt{5} + 2\sqrt{3}
\]
- This cannot be simplified to a single term.
Now, considering Sandra’s answer of \( 8\sqrt{15} \):
- She incorrectly combined the coefficients of \( 4\sqrt{5} \) and \( 2\sqrt{3} \) as if they were like terms which isn’t allowed since \( \sqrt{5} \) and \( \sqrt{3} \) are different.
Hence, the correct answer is:
**c. Sandra's answer is not correct. She should have added the coefficients to get \( 4\sqrt{5} + 2\sqrt{3} \), which does not simplify further.**