Question

Identify the power of the radicand below.
7 sq root 3 to the 4th power

Answer 1

A. 3 B. 4 C. 7 D. The radical above does not have a power.

Answer 2

\(7\sqrt{3^4}\)
Is this correct?

Answer 3

yes

Answer 4

Just be reminded of this:
\[a \sqrt[n]{b}^m = a(b)^{\frac{ m }{ n }}\]
Do you get what I mean?

Answer 5

okay

Answer 6

can you tell me if its A,B,C,D ?

Answer 7

We aren't supposed to do that. We are supposed to guide you to an answer.... and a rather obvious one too...

Answer 8

oh okay

Answer 9

Can you pick one? Among the choices.

Answer 10

i had picked C. 7

Answer 11

Can you tell us why?

Answer 12

i guess i really dont know

Answer 13

I think you must observe this example.
\[3\sqrt{5^5}\]
The exponent of this one is actually 5/2.
Radicand can be converted in terms of exponents by making the exponent of the base itself as numerator and the degree of radical as the denominator

Answer 14

\(\huge \large \sqrt[7]{3^4}\)

Answer 15

its like this right ?

Answer 16

@MarcelDatDude*

Answer 17

well i dont have all the time,
if it looks like above, then :-

\(\huge \sqrt[7]{\color{red}{3^4}}\)

Answer 18

yes

Answer 19

ty

\(\huge \color{red}{3^4}\)

is called \(\color{red}{radicand}\)

Answer 20

wat is its power ?

Answer 21

Look there's a difference between:

\(\large 7\sqrt{3^4}\) and \(\large \sqrt[7]{3^4}\)

Although it doesn't change the answer to this problem, but just for the sake of clarity. I've seen one other user ask if it was the first and you said "yes", then someone else asked if it as the second and you said "yes", but they are NOT the same.

I'll explain with a similar example:

Consider \(\large 3\sqrt{2^5}\)

Here, 3 is the coefficient of the radical expression, \(\large \sqrt{2^5}\) . \(\large 2^5\) is the "radicand", the stuff under the radical sign, and so 5 is the power of the radicand. The index of the root is 2 (square root).

Now consider: \(\large \sqrt[3]{2^5}\)

There is no coefficient. \(\large 2^5\) is the "radicand", and so 5 is the power of the radicand. The index of the root is 3 (cube root). Now, if you wrote this, instead of radical notation, in rational exponent notation, you would get: \(\large 2^{5/3}\)
Always, the POWER in the numerator of the rational exponent, the ROOT in the denominator.

But the question didn't ask you to write in exponent notation, it just asked for the "power of the radicand", which again, is the same regardless of which way the problem is written.

But I still think it's important to understand the difference. :)

Answer 22

^^ nice