Put the steps in order used to simplify the expression below

√28 + 3√63

answer choices: √4⋅7 + 3√9⋅7, √2⋅2⋅7 + 3√3⋅3⋅7 , 11√7 , 2√7 + 3 ⋅ 3√7 , 2√7 + 9√7, what is the correct order for simplifying the expression? answer 100% correctly

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To simplify the expression \(\sqrt{28} + 3\sqrt{63}\), we can follow these steps in the correct order:

1. **Factor** the square roots:
- \(\sqrt{28} = \sqrt{4 \cdot 7} = \sqrt{4} \cdot \sqrt{7} = 2\sqrt{7}\)
- \(\sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7}\)

2. **Substitute** these values back into the expression:
- So, we have \(\sqrt{28} + 3\sqrt{63} = 2\sqrt{7} + 3(3\sqrt{7})\)

3. **Multiply the coefficients**:
- \(3(3\sqrt{7}) = 9\sqrt{7}\)

4. **Combine like terms**:
- \(2\sqrt{7} + 9\sqrt{7} = (2 + 9)\sqrt{7} = 11\sqrt{7}\)

Thus, the correct order of the steps used to simplify the expression \(\sqrt{28} + 3\sqrt{63}\) is:

1. \(\sqrt{28} = \sqrt{4 \cdot 7} + 3\sqrt{63} = 3\sqrt{9 \cdot 7}\)
2. \(\sqrt{4} \cdot \sqrt{7} + 3\sqrt{9} \cdot \sqrt{7}\)
3. \(2\sqrt{7} + 3 \cdot 3\sqrt{7}\)
4. \(2\sqrt{7} + 9\sqrt{7}\)
5. \(11\sqrt{7}\)

Hence, the final correct answer is \(11\sqrt{7}\).

In conclusion, the steps in order for simplifying the expression are:

1. \(\sqrt{4 \cdot 7} + 3\sqrt{9 \cdot 7}\)
2. \(2\sqrt{7} + 3 \cdot 3\sqrt{7}\)
3. \(2\sqrt{7} + 9\sqrt{7}\)
4. \(11\sqrt{7}\)

The correct order of the answer choices would then be:
- \(\sqrt{4 \cdot 7} + 3\sqrt{9 \cdot 7}\)
- \(\sqrt{2 \cdot 2 \cdot 7} + 3\sqrt{3 \cdot 3 \cdot 7}\)
- \(2\sqrt{7} + 9\sqrt{7}\)
- \(11\sqrt{7}\)

And the last step gives you the final answer: \(11\sqrt{7}\).

anonymous anonymous answered
2 months ago

remove everything and just put the answers, also remove the ( and \

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

1. √4⋅7 + 3√9⋅7

2. √2⋅2⋅7 + 3√3⋅3⋅7
3. 2√7 + 3⋅3√7
4. 2√7 + 9√7
5. 11√7

anonymous anonymous answered
2 months ago

thank you, is that the correct order when simplifying the expression?

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

Yes, the correct order for simplifying the expression \( \sqrt{28} + 3\sqrt{63} \) is:

1. \( \sqrt{4⋅7} + 3\sqrt{9⋅7} \)
2. \( \sqrt{2⋅2⋅7} + 3\sqrt{3⋅3⋅7} \)
3. \( 2\sqrt{7} + 3⋅3\sqrt{7} \)
4. \( 2\sqrt{7} + 9\sqrt{7} \)
5. \( 11\sqrt{7} \)

So, that is the correct order for simplifying the expression.