Final answer:
The value of x for which √15 would simplify to 5√3 is 5 since multiplying 15 by 5 gives 75, which can be rewritten as (5×5)×3, hence the square root becomes 5√3.
Step-by-step explanation:
To find the value of x for which √15 would simplify to 5√3, we can use exponential rules. First, we have to recognize that both 15 and 5√3 can be expressed in terms of the same base, which is 3.
The number 15 is 3×5, and the number 5√3 is 5 times the square root of 3.
We can express 15 as 3×5 and rewite the square root of 15 as the square root of (3×5), which is the same as √3 times √5.
Since we want to express it as 5√3, we are essentially looking for the square root of (5×5×3), which would then simplify to 5√3.
Therefore, the value of x for which √(15 × x) simplifies to 5√3 is 5, because √(15 × 5) equals √(3×5×5) which simplifies to 5√3.