# What number raised to the fifth power equals 243?

Nov 9, 2015

$3$

#### Explanation:

There's not really a good way to explain this one. It's sort of guess and check, but there are a few cool tricks.

Whenever you raise something to the 5th power, the ones digit stays the same.
So basically try raising 3, 13, 23, and so on to the fifth until you get it.

Or just use a calculator.

Sep 6, 2016

$243 = {3}^{5}$

#### Explanation:

When you are dealing with an unfamiliar number, or one that is quite big, break it down into the product of its prime factors.

This is especially true when you are working with roots.

By easy short division you will find that:

$243 = 3 \times 3 \times 3 \times 3 \times 3 = {3}^{5}$

"Now the question is a piece of cake! (or EZ as "pi)

Let the unknown base be $x$

${x}^{5} = 243 = {3}^{5}$

$x = 3$

Sep 7, 2016

If you really want to go to town on this one use logs

$x = 3$

#### Explanation:

Let the unknown value be $x$

$\implies {x}^{5} = 243$

Taking logs

$5 \log \left(x\right) = \log \left(243\right)$

$\log \left(x\right) = \log \frac{243}{5}$

$x = {\log}^{- 1} \left[\log \frac{243}{5}\right]$

$x = 3$