Question

Simplify 4 fourth root of 80

Answer 1

What is 1^4 equal to

Answer 2

4?

Answer 3

no, 1^4 = 1*1*1*1 = 1

Answer 4

similarly, 2^4 = 2*2*2*2 = 16

Answer 5

3^4 = 3*3*3*3 = 81

since we overshoot 80, we stop here

so we only need to see if 2^4 = 16 goes into 80

1^4 = 1 goes into 80, but we ignore it since it's a trivial factor

Answer 6

So does 16 go into 80?

Answer 7

In other words, is 80/16 a whole number?

Answer 8

ummm no?

Answer 9

actually, 80/16 is a whole number since 80/16 = 5

Answer 10

so this tells us that 80 = 16*5

Answer 11

Your 1st question

Answer 12

why is this important? This is important because we factored 80 into two factors where one factor is a perfect 4th power


This then allows us to say this


\[\Large \sqrt[4]{80}\]


\[\Large \sqrt[4]{16*5}\]


\[\Large \sqrt[4]{16}*\sqrt[4]{5}\]


\[\Large \sqrt[4]{2^4}*\sqrt[4]{5}\]


\[\Large 2\sqrt[4]{5}\]

Answer 13

So \[\Large \sqrt[4]{80} = 2\sqrt[4]{5}\]

Answer 14

\[4 \sqrt[4]{80}\]

this is the question

Answer 15

so there's a 4 outside the 4th root?

Answer 16

If that's the case, then multiply that outer 2 by 4 to get 8