For which value of x must the expression √97x be further simplified?
do you mean
sqrt (97x)????
97 is a prime number
so if we have sqrt(97*97)
that is 97
so x = 97 works
97 times any perfect square like 4 or 9 also works
To determine the value of x for which the expression √97x should be further simplified, we need to identify if there are any perfect square factors in 97x.
First, let's determine the prime factorization of 97:
97 cannot be factored further since it is a prime number.
Now, let's analyze the expression √97x. Notice that x is multiplied by 97, but we don't know its value yet.
To simplify the expression, we want to find a value of x that has perfect square factors. This way, we can simplify the square root by taking the square root of those factors.
Since 97 is prime, there are no perfect square factors of 97 itself.
However, if x contains a perfect square factor, we can simplify the expression. For example, let's say x = 25. Then the expression becomes √97 * 25, which simplifies to 5√97.
So, to further simplify the expression √97x, you need to choose a value for x that has a perfect square factor. If x does not have a perfect square factor, the expression cannot be simplified any further.
Who says it has to be simplified at all?
However, since 97 is prime, 97x is a perfect square if x is 97.
Or, if x is 97 times any perfect square.