Question

FAN AND MEDAL! EASY QUESTION!
is the 4th square root the same as to the 1/4 power? meaning that 2^1/2 = the forth squair root or 2?

Answer 1

@amistre64

Answer 2

@mathslover @phi @Callisto please help! its really just a technical question.

Answer 3

@terenzreignz

Answer 4

yes

Answer 5

2^1/2 = sqrt(2)

2^1/4 = 4rt(2)

k^1/n = nrt(k)

Answer 6

that's what I thought, thank you :)

Answer 7

Here is how you know

First, remember when you multiply numbers with the same base, you add their exponents. Example:
\[2^1 \cdot 2^1 = 2^{1+1}= 2^2 \text{ or } 4 \]

Second, by definition, the fourth root of 2 (call it a) means
\[ a \cdot a \cdot a \cdot a= 2\]

Third, let's multiply 2^(¼) times itself 4 times:
\[ 2^{\frac{1}{4}} \cdot 2^{\frac{1}{4}} \cdot 2^{\frac{1}{4}} \cdot 2^{\frac{1}{4}} =
2^{\frac{1}{4}+\frac{1}{4}+\frac{1}{4}+\frac{1}{4}}= 2^{\frac{4}{4}}= 2^1=2
\]

in other words, 2^(¼) must be the fourth root of 2, because when we multiply it by itself 4 times, we get 2