Question

help please((: fan and medal

1. find all the real roots of - 9/16

2. find all the real cube roots of -0.000125

Answer 1

the number is negative right?

Answer 2

the fraction is negative

Answer 3

remember there are no REAL roots of a negative number

Answer 4

I assume that is supposed to be real SQUARE roots of -9/16.

Answer 5

yes

Answer 6

but you can calulate the value for the second one

Answer 7

So @FaiqRaees is correct — there are no real numbers which when multiplied by themselves give you a negative answer, right?

\[(-1)*(-1) = |-1|*|-1| = 1*1 = 1\]and the same is true for any other negative number

But if you multiply a negative number with itself twice:
\[(-1)*(-1)*(-1) = ((-1)*(-1))*(-1)\]but we know that \((-1)*(-1) = 1\) so we can write that as \[(-1)*(-1)*(-1) = (1)*(-1) = -1\]

that means we can find a cube root of a negative number, and it will be a negative number.

For example, \[\sqrt[3]{-8}=-2\]because \[(-2)*(-2)*(-2) = -8\]

Answer 8

first break the number into factors
0.000125
0.000001*125
Now apply the cube root on both the number
0.01*5
now apply the negative sign and multiply them
-0.05

Answer 9

another way to the same answer, if you remember that \[\frac{1}{8}=0.125\]I told you that \[\sqrt[3]{-8}=-2\]which implies that \[\sqrt[3]{8}=2\]and from that \[\frac{1}{\sqrt[3]{8}} = \frac{1}{2}\]
We also know that \[10*10*10=1000\]so\[\frac{1}{10}*\frac{1}{10}*\frac{1}{10} = \frac{1}{1000}\]

therefore
\[0.000125=0.001*0.125 = \frac{1}{1000}*\frac{1}{8}\]and \[\sqrt[3]{0.000125}=\sqrt[3]{\frac{1}{1000}*\frac{1}8} = \sqrt[3]{\frac{1}{1000}}\sqrt[3]{*\frac{1}8} =\frac{1}{10}*\frac{1}{2} = \frac{1}{20} = 0.05\]

We wanted to do the cube root of \(-0.000125\), so we can find the cube root of \(0.000125\) and just slap on the negative sign.
\[\sqrt[3]{-0.000125}=-\sqrt[3]{0.000125} = -0.05\]

That may seem like it was a long path, but if you recognize that number as a fraction (as I laboriously spelled out), you can write the answer down on the spot.