Question

5^4 the square root of 32 - the 4th square root 162

Answer 1

\(\color{#000000}{ \displaystyle 5\sqrt[4]{32}-\sqrt[4]{162} }\) ?

Answer 2

like that?

Answer 3

\[5\sqrt[4]{32} - \sqrt[4]{162}\]

Answer 4

Hint: \(\color{#000000}{ \displaystyle 162=2\cdot 3^4 }\)

Answer 5

Also, \(\color{#000000}{ \displaystyle 32=2^5=2\cdot 2^4 }\)

Answer 6

So, you can brake this the following way.

\(\color{#000000}{ \displaystyle 5\sqrt[4]{32}-\sqrt[4]{162} }\)

\(\color{#000000}{ \displaystyle 5\sqrt[4]{2\times 2^4}-\sqrt[4]{2\times 3^4} }\)

\(\color{#000000}{ \displaystyle \{5\sqrt[4]{2}\times 5\sqrt[4]{ 2^4}\}-\{\sqrt[4]{2}\times \sqrt[4]{ 3^4} \} }\)

Answer 7

Note that \(\color{#000000}{ \displaystyle \sqrt[4]{2^4}=2 }\) and \(\color{#000000}{ \displaystyle \sqrt[4]{3^4}=3 }\).

Answer 8

and then all there will be left is to add like terms.

Answer 9

this does not make any sense

Answer 10

oh well

Answer 11

look you don't have to get smart with me...