If x= √3, find the value of x⁴.

9

Step-by-step explanation:

Hi there!

We're given that x=√3, and we want to find the value of

We can substitute √3 as x, and then raise it to the 4th power, but if you don't know what that number is, it might be difficult to figure it out.

An easier way would be to write as x² * x², which in that case, we can multiply √3 by itself, multiply √3 by itself again, and then multiply those 2 numbers together.

If we do it this way, it'll look something like this (remember: x² is equal to x*x, or (x)²:

(√3)² * (√3)²

The order of operations will ask us to first take care of what's in the parentheses, and then to raise the numbers to their powers. Starting with the number on the left of the multiplication sign,

(√3)² = (√3)(√3)=3

And then the number on the right of the multiplication sign:

(√3)² = (√3)(√3)=3

Substitute these numbers in as (√3)² and (√3)²:

3 * 3 = 9

Therefore, x² * x², or is equal to 9

Hope this helps!