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OLga [1]
3 years ago
6

Giving brainliest to the answer who gives step by step examples clearly!

Mathematics
2 answers:
Anarel [89]3 years ago
7 0

<em>Hi there!</em>

<em>This should be easy,lol!</em>

<em>Answer:</em>

<em />\sqrt[3]{-128} = \boxed{-128 \sqrt{3} }<em> (Decimal: -221.702503)</em>

<em />\sqrt[3]{162} = \boxed{162 \sqrt{3} }<em> (Decimal: 280.592231)</em>

<em />\sqrt[3]{-1000x^4} = \boxed{-1732.050808x^4}<em />

<em>Sorry bout the explanation thingy. Their really long -.-!</em>

<em>But the last one is short so i'll put it for you!</em>

<em>Step-by-step explanation:</em>

<em>∴!For the last one!∴</em>

<em />\sqrt[3]{-1000x^4}<em />

<em>Simplifies to:</em>

<em />= - 1732.050808 * x^4<em />

<em />= - 1732.050808 * ( x * x * x * x)<em> </em>

<em />= - 1732.050808x^4<em />

<em>Have a great day/night!</em>

Digiron [165]3 years ago
7 0

Answer:

10)

=-4\sqrt[3]{2}

12)

=3\sqrt[3]6

14)

=-10x\sqrt[3]{x}

Step-by-step explanation:

10)

We have:

\sqrt[3]{-128}

We want to simplify the cube root. So, let's start picking at the factors.

Notice that -128 is divisible by 64. So:

=\sqrt[3]{-1\cdot64\cdot2}

Now, notice that 64 is the same as 4³. (-1) is also the same as (-1)³. Therefore:

=\sqrt{(-1)^3\cdot(4)^3\cdot2

We can now expand our root:

=\sqrt[3]{(-1)^3}\cdot\sqrt[3]{(4)^3}\cdot\sqrt[3]{2}

The cubes and the cube roots cancel each other out. This leaves us with:

=(-1)\cdot(4)\cdot\sqrt[3]2

Simplify:

=-4\sqrt[3]{2}

12)

We have:

\sqrt[3]{162}

Again, let's see what we can factor out.

If it's unclear what we can factor out, we can guess and check. Since 162 is even, let's divide it by 2. This yields:

=\sqrt[3]{2\cdot81}

Notice here that 81 is the same as 3⁴. Therefore:

=\sqrt[3]{2\cdot3^4}

We can separate the 3 from the exponent using the properties of exponents:

=\sqrt[3]{2\cdot3\cdot3^3}

Expand:

=\sqrt[3]{3^3}\cdot\sqrt[3]{2\cdot3}

The cube roots and cube will cancel. This leaves us with:

=3\cdot\sqrt{2\cdot3}

Simplify:

=3\sqrt[3]6

14)

We have:

\sqrt[3]{-1000x^4}

Notice here that 1000 is the same as 10³. Also, we can separate an x from the x⁴. Therefore:

=\sqrt[3]{-1\cdot (10)^3\cdot x^3\cdot x}

Also, (-1) is the same as (-1)³. Thus:

=\sqrt[3]{(-1)^3\cdot (10)^3\cdot x^3\cdot x}

Expand:

=\sqrt[3]{(-1)^3}\cdot\sqrt[3]{(10)^3}\cdot\sqrt[3]{x^3}\cdot\sqrt[3]{x}

The cube roots and the cube will cancel. This leaves us with:

=-1\cdot10\cdot x\cdot\sqrt[3]{x}

Simplify:

=-10x\sqrt[3]{x}

And we're done!

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