Question

Given that n^2/3 = 8 and n> 0

work out the value of n.

Give your answer in the form a square root b where a and b are integers.

Answer 1

16
`√(2)`

Explanation:

Using the rule of exponents/ radicals

`a^{(m)/(n) }` =
`\sqrt[n]{a^(m) }` , then

`n^{(2)/(3) }` =
`\sqrt[3]{n^2}` , then

`\sqrt[3]{n^2}` = 8 ( cube both sides )

n² = 8³ ( take the square root of both sides )

n =
`√(8^3)`

=
`√(512)`

=
`√(256(2))`

=
`√(256)` ×
`√(2)`

= 16
`√(2)`