Question

I need help on a problem

Answer 1

To simplify the radical, factorize the number under it using the prime number

Since 252 is an even number, then let us divide it by the 1st prime number 2

$\frac{252}{2}=126$

since 126 is an even number, then divide it by 2 again

$\frac{126}{2}=63$

Now 63 is an odd number and sum of its digit = 6 + 3 = 9, then

Divide it by the 2nd prime number 3

$\frac{63}{3}=21$

Since 21 is divisible by 3, divide it by 3 again

$\frac{21}{3}=7$

Then 252 = 2 x 2 x 3 x 3 x 7, put them under the radical

$\sqrt[]{252}=\sqrt[]{2\times2\times3\times3\times7}$

Each number repeated twice can go out the radical, then

2 and 3 will go out the radical

$\begin{gathered} \sqrt[]{252}=2\times3\times\sqrt[]{7} \\ \sqrt[]{252}=6\sqrt[]{7} \end{gathered}$

The simplest form of the radical is 6 square root 7

$\begin{gathered} \sqrt[]{252}=\sqrt[]{4}\times\sqrt[]{63} \\ =2\times\sqrt[]{63} \\ =2\times\sqrt[]{9}\times\sqrt[]{7} \\ =2\times3\times\sqrt[]{7} \\ =6\times\sqrt[]{7} \\ =6\sqrt[]{7} \end{gathered}$