1. Multiply 93 −−√ ⋅67–√%0D%0A9%0D%0A3%0D%0A %0D%0A %0D%0A⋅%0D%0A6%0D%0A7%0D%0A. Give an exact answer.(1 point)

Question

2. Multiply 11 −−−√ ⋅67–√ . Give an exact answer.(1 point)

3. Divide 2√65/√5. Provide an exact answer. (1 point)

4. Divide 9√33/27√11. Provide an exact answer. (1 point)

5. Simplify 7√99.(1 point)

Answer 1

Let's solve each of the problems step by step.

1. Multiply \( \sqrt{93} \cdot \sqrt{67} \)

   \[ \sqrt{93} \cdot \sqrt{67} = \sqrt{93 \cdot 67} \]

   Now calculate \( 93 \cdot 67 \):

   \[ 93 \cdot 67 = 6231 \]

   So the exact answer is:

   \[ \sqrt{6231} \]

2. Multiply \( \sqrt{11} \cdot \sqrt{67} \)

   \[ \sqrt{11} \cdot \sqrt{67} = \sqrt{11 \cdot 67} \]

   Now calculate \( 11 \cdot 67 \):

   \[ 11 \cdot 67 = 737 \]

   So the exact answer is:

   \[ \sqrt{737} \]

3. Divide \( \frac{2\sqrt{65}}{\sqrt{5}} \)

   You can simplify by multiplying numerator and denominator by \( \sqrt{5} \):

   \[ \frac{2\sqrt{65}}{\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{2\sqrt{65 \cdot 5}}{5} = \frac{2\sqrt{325}}{5} \]

   Since \( 325 = 25 \cdot 13 \):

   \[ = \frac{2 \cdot \sqrt{25 \cdot 13}}{5} = \frac{2 \cdot 5 \cdot \sqrt{13}}{5} = 2\sqrt{13} \]

   So the exact answer is:

   \[ 2\sqrt{13} \]

4. Divide \( \frac{9\sqrt{33}}{27\sqrt{11}} \)

   This can be simplified by dividing both the numerator and the denominator:

   \[ \frac{9}{27} = \frac{1}{3} \]

   The square root part can also be simplified:

   \[ \frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3} \]

   Thus the answer becomes:

   \[ \frac{1}{3}\sqrt{3} \]

   So, the exact answer is:

   \[ \frac{\sqrt{3}}{3} \]

5. Simplify \( 7\sqrt{99} \)

   First factor \( 99 \):

   \[ 99 = 9 \cdot 11 = 3^2 \cdot 11 \]

   Now we can simplify:

   \[ 7\sqrt{99} = 7\sqrt{9 \cdot 11} = 7\sqrt{9} \cdot \sqrt{11} = 7 \cdot 3 \sqrt{11} = 21\sqrt{11} \]

   So the exact answer is:

   \[ 21\sqrt{11} \]

In summary, the answers are:

1. \( \sqrt{6231} \)
2. \( \sqrt{737} \)
3. \( 2\sqrt{13} \)
4. \( \frac{\sqrt{3}}{3} \)
5. \( 21\sqrt{11} \)

Answer 2

wait let me re ask 1. and 2.
1. 9sqrt3 x 6sqrt7
2. sqrt11 x 6sqrt7

Answer 3

Sure! Let's solve the revised problems.

1. Multiply \( 9\sqrt{3} \times 6\sqrt{7} \)

   To multiply these expressions, multiply the coefficients and the square root parts separately:

   \[ 9 \times 6 \times \sqrt{3} \times \sqrt{7} = 54 \times \sqrt{3 \cdot 7} \]

   Simplifying the square root:

   \[ \sqrt{3 \cdot 7} = \sqrt{21} \]

   Therefore:

   \[ 9\sqrt{3} \times 6\sqrt{7} = 54\sqrt{21} \]

   So the exact answer is:

   \[ 54\sqrt{21} \]

2. Multiply \( \sqrt{11} \times 6\sqrt{7} \)

   Similar to the previous problem, multiply the coefficients and the square root parts:

   \[ \sqrt{11} \times 6\sqrt{7} = 6 \times \sqrt{11} \times \sqrt{7} = 6 \times \sqrt{11 \cdot 7} \]

   Simplifying the square root:

   \[ \sqrt{11 \cdot 7} = \sqrt{77} \]

   Thus:

   \[ \sqrt{11} \times 6\sqrt{7} = 6\sqrt{77} \]

   So the exact answer is:

   \[ 6\sqrt{77} \]

In summary, the answers are:

1. \( 54\sqrt{21} \)
2. \( 6\sqrt{77} \)

Answer 4

now what about 4.?

4. 9sqrt33/27sqrt11

Answer 5

Let's simplify the expression \( \frac{9\sqrt{33}}{27\sqrt{11}} \).

1. Simplify the coefficients: \[ \frac{9}{27} = \frac{1}{3} \]

2. Simplify the square roots: \[ \frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3} \]

3. Put it all together: \[ \frac{9\sqrt{33}}{27\sqrt{11}} = \frac{1}{3} \cdot \sqrt{3} = \frac{\sqrt{3}}{3} \]

So the exact answer is:

\[ \frac{\sqrt{3}}{3} \]

Answer 6

what do you mean /sqrt33? like fraction?? so you mean 1/sqrt33? or JUST sqrt33

Answer 7

I apologize for any confusion. Let's clarify the evaluation of the expression more clearly. Given your expression is:

\[ \frac{9\sqrt{33}}{27\sqrt{11}} \]

We were simplifying this expression, which is indeed a fraction.

1. Separate the coefficients from the square roots: \[ \frac{9}{27} = \frac{1}{3} \]

2. Simplify the square roots: \[ \frac{\sqrt{33}}{\sqrt{11}} = \sqrt{\frac{33}{11}} = \sqrt{3} \]

3. Combine the results: \[ \frac{9\sqrt{33}}{27\sqrt{11}} = \frac{1}{3} \cdot \sqrt{3} = \frac{\sqrt{3}}{3} \]

So, the expression \( \frac{9\sqrt{33}}{27\sqrt{11}} \) simplifies to:

\[ \frac{\sqrt{3}}{3} \]

If you were asking about a different expression or format (like asking for \( \frac{1}{\sqrt{33}} \)), please clarify, and I will be happy to help!

Answer 8

but what do you mean by /sqrt33?? i did 1/sqrt33 so its as a fraction its not the answer then i did sqrt33 not right either so is it really just the fraction /sqrt33 like nothing on top of the line?

Answer 9

Thank you for your patience! Let's clarify.

In the expression you provided, \( \frac{9\sqrt{33}}{27\sqrt{11}} \), my previous response may have caused some confusion regarding what "over" means.

• What I meant is that there is a fraction involved, and you correctly identified it as \( \frac{9\sqrt{33}}{27\sqrt{11}} \).

In this case:

• The entire expression \( \frac{9\sqrt{33}}{27\sqrt{11}} \) is indeed a fraction.
• The numerator is \( 9\sqrt{33} \), and the denominator is \( 27\sqrt{11} \).

The simplification steps I provided were correct, resulting in \( \frac{\sqrt{3}}{3} \).

Key Takeaway:

• The fraction \( \frac{9\sqrt{33}}{27\sqrt{11}} \) simplifies to \( \frac{\sqrt{3}}{3} \).

If you were looking for \( \frac{1}{\sqrt{33}} \), that would be a different expression entirely. But in this context, we were working with \( 9\sqrt{33} \) divided by \( 27\sqrt{11} \).

Final Conclusion: The final simplified answer for your expression \( \frac{9\sqrt{33}}{27\sqrt{11}} \) is:

\[ \frac{\sqrt{3}}{3} \]

If this still doesn't address your concerns, please let me know!

Answer 10

oh jeez your confusing its sqrt3/3 LIKE THAT.

1. 54sqrt21
2. 6sqrt77
3. 2sqrt13
4. sqrt3/3
5. 21sqrt11

Answer 11

Thank you for your clarification, and I apologize for any confusion caused in my previous responses. Let's summarize all your answers clearly:

1. \( 9\sqrt{3} \times 6\sqrt{7} = 54\sqrt{21} \)

2. \( \sqrt{11} \times 6\sqrt{7} = 6\sqrt{77} \)

3. \( \frac{2\sqrt{65}}{\sqrt{5}} = 2\sqrt{13} \)

4. \( \frac{9\sqrt{33}}{27\sqrt{11}} = \frac{\sqrt{3}}{3} \)

5. \( 7\sqrt{99} = 21\sqrt{11} \)

You've summarized your answers correctly! Thank you for your patience as we worked through the clarifications together. If you have any more questions or need further assistance, feel free to ask!