Zubin drew a circle with right triangle PRQ inscribed in it, as shown below: The figure shows a circle with points P, Q, and R o
1 answer:
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Given:
Expression is
To prove:
If r is any rational number, then is rational.
Step-by-step explanation:
Property 1: Every integer is a rational number. It is Theorem 4.3.1.
Property 2: The sum of any two rational numbers is rational. It is Theorem 4.3.2.
Property 3: The product of any two rational numbers is rational. It is Exercise 15 in Section 4.3.
Let r be any rational number.
We have,
It can be written as
Now,
3, -2 and 4 are rational numbers by property 1.
is rational by Property 3.
are rational by Property 3.
is rational by property 2.
So, is rational.
Hence proved.
To take out terms outside the radical we need to divide the power of the term by the index of the radical; the quotient will be the power of the term outside the radical, and the remainder will be the power of the term inside the radical.
First, lets factor 8:
Now we can divide the power of the term, 3, by the index of the radical 2:
= 1 with a remainder of 1
Next, lets do the same for our second term
:
= 3 with a remainder of 1
Again, lets do the same for our third term
:
with no remainder, so this term will come out completely.
Finally, lets take our terms out of the radical:
We can conclude that the correct answer is the third one.
First, lets factor 8:
Now we can divide the power of the term, 3, by the index of the radical 2:
Next, lets do the same for our second term
Again, lets do the same for our third term
Finally, lets take our terms out of the radical:
We can conclude that the correct answer is the third one.