Fine the cube root of -729: 3√-729

The cube root of -729 can be calculated as follows:

\[ \sqrt[3]{-729} = -\sqrt[3]{729} \]

Since \(729\) is \(9^3\) (because \(9 \times 9 \times 9 = 729\)), we have:

\[ \sqrt[3]{729} = 9 \]

Therefore,

\[ \sqrt[3]{-729} = -9 \]

So, the cube root of -729 is \(-9\).

find the cube root of -8: 3√-8

To find the cube root of \(-8\), we can write it as:

\[ \sqrt[3]{-8} = \sqrt[3]{-2^3} \]

Since the cube root of a negative number is also negative, we have:

\[ \sqrt[3]{-2^3} = -2 \]

Therefore, the cube root of \(-8\) is \(-2\).

find the cubic root of 135

To find the cube root of \(135\), you would typically use the notation:

\[ \sqrt[3]{135} \]

The cube root of \(135\) can be approximated, as \(135\) is not a perfect cube. You can calculate it using a calculator, or estimate it by finding two nearby perfect cubes.

The perfect cubes near \(135\) are \(125\) (which is \(5^3\)) and \(216\) (which is \(6^3\)). Since \(135\) is between \(125\) and \(216\), we know that:

\[ 5 < \sqrt[3]{135} < 6 \]

To get a more precise value, you can use a calculator:

\[ \sqrt[3]{135} \approx 5.13 \]

Thus, the approximate value of the cube root of \(135\) is about \(5.13\).

find the cubic root of 135
5 cubic root 3√27
3 cubic root 3√5
3√5
cubic root 3√5

It looks like you're asking for the cube root of \(135\) in a simplified form. Let's break this down step by step.

1. First, we know that \(135\) can be factored into prime factors:

\[ 135 = 3^3 \times 5 \]

2. Now, we can find the cube root of \(135\):

\[ \sqrt[3]{135} = \sqrt[3]{3^3 \times 5} \]

3. Since the cube root of \(3^3\) is \(3\), we have:

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

So, the cube root of \(135\) can be expressed as:

\[ \sqrt[3]{135} = 3 \sqrt[3]{5} \]

To summarize,

\[ \sqrt[3]{135} = 3 \sqrt[3]{5} \]

If you were referring to something else or need another specific form, please clarify!

what is the circumference of a circle with a diameter of 4.5 miles? estimate the circumference to the hundredths place or using 3.14 for pi

To calculate the circumference of a circle, you can use the formula:

\[ C = \pi \times d \]

where \(C\) is the circumference and \(d\) is the diameter.

Given that the diameter is \(4.5\) miles and using \(\pi \approx 3.14\):

\[ C = 3.14 \times 4.5 \]

Now, perform the multiplication:

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

So, the estimated circumference of a circle with a diameter of \(4.5\) miles is approximately 14.13 miles.

rewrite the irrational cube root 3√189 as the product of an integer and another irrational cube root. show your work.

To rewrite the irrational cube root \(\sqrt[3]{189}\) as the product of an integer and another irrational cube root, we first need to factor \(189\) into its prime factors.

1. Factor \(189\):

   • \(189\) can be divided by \(3\): \[ 189 \div 3 = 63 \]
   • Then, factor \(63\) by dividing by \(3\) again: \[ 63 \div 3 = 21 \]
   • Finally, factor \(21\) by dividing by \(3\): \[ 21 \div 3 = 7 \]
   • The complete factorization of \(189\) is: \[ 189 = 3^3 \times 7 \]

2. Express \(\sqrt[3]{189}\): \[ \sqrt[3]{189} = \sqrt[3]{3^3 \times 7} \]

3. Apply the property of cube roots:

   • We can separate the expression using the property of cube roots: \[ \sqrt[3]{189} = \sqrt[3]{3^3} \times \sqrt[3]{7} \]

4. Simplify the cube root:

   • Since \(\sqrt[3]{3^3} = 3\), we get: \[ \sqrt[3]{189} = 3 \times \sqrt[3]{7} \]

Thus, the expression \(\sqrt[3]{189}\) can be rewritten as:

\[ \sqrt[3]{189} = 3\sqrt[3]{7} \]

This shows \(\sqrt[3]{189}\) as the product of an integer (\(3\)) and another irrational cube root (\(\sqrt[3]{7}\)).