Question

How do you simplify the square root of $243$?

Answer 1

Find the simplified form of the square root by using the prime factorization.

To simplify the square root of $243$ means to get the simplest radical form of$\surd 243.$

List the factors of $243$ like so:

$1,3,9,27,81,243$

Identify the perfect squares from the list of factors above:

$1,9,81$

Divide$243$ by the largest perfect square found in the previous step:

$\frac{243}{81}=3..\left(1\right)$

Calculate the square root of the largest perfect square:

$\surd 81=9...\left(2\right)$

Use the equation $1\&2$ to get the square root of $243$in its simplest form $9\surd 3$

Hence, the square root of $243$ written in simplified form is $9\surd 3$.