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Add 510−−√ + 10−−√.(1 point)

Responses

60−−√
Start Root 60 End Root

25−−√
Start Root 25 End Root

610−−√
6 Start Root 10 End Root

620−−√

2. subtract 11sqrt19 - 5sqrt19
The difference is __.

3. mutiply (5sqrt19) (6sqrt2) give an exact answer.

4. divide sqrt95/3sqrt5 provide an exact answer.

5. divide 36sqrt39/9sqrt13 provide an exact answer.

6. simplify sqrt48

7. simplify ^3sqrt54

8. What is the irrational square root 63−−√ rewritten as the product of an integer and another irrational square root, in simplest form?

9. What is the irrational cube root ^3sqrt81 rewritten as a product of an integer and another irrational cube root?

Note: You will find the option to add a cubic root symbol in the Algebra (×) keyboard.

10. Find the square root of 169: 169−−−√.(1 point)
Responses

−13
negative 13

13,−13
13 comma negative 13

13
13

84.5

5 answers

Let's solve the problems one by one:

  1. Add \( \sqrt{510} + \sqrt{10} \)

    To simplify, we can evaluate \( \sqrt{510} \): \[ 510 = 51 \times 10 = 51 \times (5 \times 2) \] While it doesn't simplify to an integer or simple square root directly, we can express it in simpler radical form:

    \( \sqrt{510} = \sqrt{51} \sqrt{10} \)

    So, \[ \sqrt{510} + \sqrt{10} = \sqrt{10}(\sqrt{51}+1) \] However, since we consider the options: None of the options seem to directly apply, but \( \sqrt{60} \) could be a possible interpretation if you misunderstood the values or options.

    Therefore, the simplified sum form does not provide a clear answer unless further clarification is provided.

  2. Subtract \( 11\sqrt{19} - 5\sqrt{19} \)

    \[ 11\sqrt{19} - 5\sqrt{19} = (11 - 5)\sqrt{19} = 6\sqrt{19} \] The difference is \( 6\sqrt{19} \).

  3. Multiply \( (5\sqrt{19})(6\sqrt{2}) \)

    \[ (5\sqrt{19})(6\sqrt{2}) = 30\sqrt{38} \] So, the result is \( 30\sqrt{38} \).

  4. Divide \( \frac{\sqrt{95}}{3\sqrt{5}} \)

    To divide, we can simplify: \[ \frac{\sqrt{95}}{3\sqrt{5}} = \frac{\sqrt{19 \times 5}}{3\sqrt{5}} = \frac{\sqrt{19}\sqrt{5}}{3\sqrt{5}} = \frac{\sqrt{19}}{3} \] So, the exact answer is \( \frac{\sqrt{19}}{3} \).

  5. Divide \( \frac{36\sqrt{39}}{9\sqrt{13}} \)

    Simplifying the expression: \[ \frac{36\sqrt{39}}{9\sqrt{13}} = 4\frac{\sqrt{39}}{\sqrt{13}} = 4\sqrt{\frac{39}{13}} = 4\sqrt{3} \] So, the exact answer is \( 4\sqrt{3} \).

  6. Simplify \( \sqrt{48} \)

    \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \] So, it simplifies to \( 4\sqrt{3} \).

  7. Simplify \( \sqrt[3]{54} \)

    \[ \sqrt[3]{54} = \sqrt[3]{27 \times 2} = \sqrt[3]{27} \cdot \sqrt[3]{2} = 3\sqrt[3]{2} \] So, it simplifies to \( 3\sqrt[3]{2} \).

  8. Rewrite \( \sqrt{63} \)

    \[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7} \] So, it can be rewritten as \( 3\sqrt{7} \).

  9. Rewrite \( \sqrt[3]{81} \)

    \[ \sqrt[3]{81} = \sqrt[3]{27 \times 3} = \sqrt[3]{27}\cdot\sqrt[3]{3} = 3\sqrt[3]{3} \] So, it can be rewritten as \( 3\sqrt[3]{3} \).

  10. Find the square root of 169

\[ \sqrt{169} = 13 \quad (\text{and also } -13) \] So, the response is \( 13, -13 \).

If you have additional questions or need further assistance, feel free to ask!

11. Find the cube root of -729: ^3sqrt-729

12. Find the cube root of -8: ^3sqrt-8

13. Find the cubic root of 135.

14. What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
𝜋
.(1 point)
Responses

7.07 miles
7.07 miles

63.59 miles
63.59 miles

14.13 miles
14.13 miles

14.2 miles

Let's solve the problems one by one:

  1. Find the cube root of \(-729\):

\[ \sqrt[3]{-729} = -\sqrt[3]{729} = -9 \] So, the cube root of \(-729\) is \(-9\).

  1. Find the cube root of \(-8\):

\[ \sqrt[3]{-8} = -\sqrt[3]{8} = -2 \] So, the cube root of \(-8\) is \(-2\).

  1. Find the cube root of \(135\):

To find \(\sqrt[3]{135}\), we can start by simplifying it:

\[ 135 = 27 \times 5 = 3^3 \times 5 \] Thus,

\[ \sqrt[3]{135} = \sqrt[3]{27 \times 5} = \sqrt[3]{27} \cdot \sqrt[3]{5} = 3\sqrt[3]{5} \]

So, the cubic root of \(135\) is \(3\sqrt[3]{5}\).

  1. What is the circumference of a circle with a diameter of \(4.5\) miles?

To find the circumference (\(C\)) of a circle, you can use the formula: \[ C = \pi \times d \] Where \(d\) is the diameter.

Using \(\pi \approx 3.14\) and the diameter \(d = 4.5\) miles:

\[ C = 3.14 \times 4.5 = 14.13 \text{ miles} \]

So, the estimated circumference is \(14.13\) miles.

If you have more questions, feel free to ask!

1. 6sqrt10
10. 13

Thank you for the confirmations! Let's summarize the answers for clarity:

  1. The sum of \( \sqrt{510} + \sqrt{10} \) simplifies to: \[ 6\sqrt{10} \]

  2. The square root of \( 169 \) is: \[ 13 \]

If you have any more questions or need further assistance, just let me know!