Find all the real cube roots of -0.000125 a)0.0025 and -0.0025 b)-0.05 and 0.05 c)-0.05 d)0.0025

Answers

We calculate the cube root, 

we know that

-0.000125> is equal to -125/1000000>(-5³/10^6)
∛(-5³/10^6) = -5/10^2> -5/100> -0.05

The answer is -0.05
Find all the real square roots of -9/16. 
= 3/4

Find all the real cube roots of -0.000125.
= -0.05

Simplify √(36g^6).

= 6 g^3

Simplify ∛(125x^21y^24).
= 5x^7y^8

Simplify √((27x^4)/(75y^2)).

    3x^2

     5y

The correct option is c.

Step-by-step explanation:

We have to find the cube roots of -0.000125.

It can be written as

\sqrt[3]{-0.000125}

\sqrt[3]{-0.000125}=-\sqrt[3]{0.000125}

\sqrt[3]{-0.000125}=-\sqrt[3]{0.05\times 0.05\times 0.05}

\sqrt[3]{-0.000125}=-\sqrt[3]{(0.05)^3}

\sqrt[3]{-0.000125}=-0.05

Therefore option c is correct.

Answer : The real cube roots of -0.000125 is, -0.05

Step-by-step explanation :

Cube root : It is defined as the number which produces a given number when cubed.

For example :

3 cubed is 27, so the cube root of 27 is 3

We Can also cube negative numbers.

For example :

When we cube +5 we get, +125 :(+5) × (+5) × (+5) = +125

When we cube -5 we get, -125 : (-5) × (-5) × (-5) = -125

So, the cube root of -125 is, -5

As we are given the number -0.000125. Now we have to determine the real cube roots of this number.

-0.000125=-\frac{125}{1000000}=-\frac{125}{10^6}

Now taking cube root of this number, we get:

-\sqrt[3]{\frac{125}{10^6}}=-\sqrt[3]{\frac{(5)^3}{10^6}}=-\frac{5}{10^2}=-0.05

Thus, the real cube roots of -0.000125 is, -0.05

\sqrt[3]{-0.000125}=-0.05

Step-by-step explanation:

We are given

\sqrt[3]{-0.000125}

Firstly, we will find factors of -0.000125

we can write as

-0.000125=(-0.05)\times (-0.05)\times (-0.05)

-0.000125=(-0.05)^3

now, we can replace it

\sqrt[3]{-0.000125}=\sqrt[3]{(-0.05)^3}

now, we can simplify it

and we get

\sqrt[3]{-0.000125}=-0.05

So,

answer is

c. -0.05

1)  \sqrt{\frac{-9}{16}}=\pm\frac{3}{4}i

2)  \sqrt[3]{-0.000125}=-0.05

3) \sqrt{(36g^6)}=6(g^3)

4) \sqrt[3]{125x^{21}y^{24}}=5(x^{7})(y^{8})

5) \sqrt{\frac{27x^4}{75y^2}}=\frac{3(x^2)}{5y}

Step-by-step explanation:

To find : The following expression

1) Find all the real square roots of -9/16.

\sqrt{\frac{-9}{16}}

There is no real roots because \sqrt{-1}=i is an imaginary number

Therefore,  \sqrt{\frac{-9}{16}}=\pm\frac{3}{4}i

2) Find all the real cube roots of -0.000125.

\sqrt[3]{-0.000125}

There is a real roots.

Therefore,  \sqrt[3]{-0.000125}=-0.05

3) Simplify \sqrt{(36g^6)}

=\sqrt{(36g^6)}

=\sqrt{6^2(g^3)^2}

=6(g^3)

Therefore, simplified form is \sqrt{(36g^6)}=6(g^3)

4) Simplify \sqrt[3]{125x^{21}y^{24}}

=\sqrt[3]{125x^{21}y^{24}}

=\sqrt[3]{5^3(x^{7})^3(y^{8})^3}

=5(x^{7})(y^{8})

Therefore, simplified form is \sqrt[3]{125x^{21}y^{24}}=5(x^{7})(y^{8})

5) Simplify \sqrt{\frac{27x^4}{75y^2}

=\sqrt{\frac{27x^4}{75y^2}

=\sqrt{\frac{9(x^2)^2}{25y^2} (Divide nr. and dr. by 3)

=\sqrt{\frac{3^2(x^2)^2}{5^2y^2}

=\frac{3(x^2)}{5y}

Therefore, simplified form is \sqrt{\frac{27x^4}{75y^2}}=\frac{3(x^2)}{5y}

-0.05

Step-by-step explanation:

This will become much easier if we can get the ugly decimal into a nice fraction form.

Start by recognising \frac{1}{8}=0.125. This is almost correct except the fraction is out by some number of factors of 10 (because the 125 part is correct but the number of 0s isn't).

\frac{1}{80} = 0.0125\\\frac{1}{800}=0.00125\\\frac{1}{8000}=0.000125

And hence we see that -0.000125=-\frac{1}{8000} and now the cube root becomes easy to compute:

\sqrt[3]{-0.000125} = \sqrt[3]{\frac{-1}{8000}} = \frac{\sqrt[3]{-1}}{\sqrt[3]{8000}} = \frac{-1}{20} = -0.05.

Advanced: You ask for all real cube roots. however the function y=\sqrt[3]{x} is described as bijective. This means for all x, there is only one y corresponding to it. (And also for all y there is only one x corresponding to that). This means there can only ever be one cube root of any real number.

We have the value -0.000125

Since this is negative value the cube number cannot be positive since it will not give an negative answer

hence the answer should be a negative number

this already eliminates the option A, B and D

now we have

 \sqrt[3]{-0.000125}

 \sqrt[3]{(-0.05).(-0.05).(-0.05)}

=-0.05 (option C)



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