Question

( 15 ^ 1/4 / 3 ^1/2) -2 Simplify​
O 3/5
O 5/3
O 25/3
O 9/5"

Answer 1

To simplify (15 ^ 1/4 / 3 ^1/2) -2, we take the fourth root of 15 and divide by the square root of 3, then subtract 2. Simplification leads to the result which is a little greater than 1 minus 2, thus producing a negative number, indicating an issue with the provided choices.

Step-by-step explanation:

To simplify the expression (15 ^ 1/4 / 3 ^1/2) -2, we first need to address each component:

• 15 ^ 1/4 is the fourth root of 15, which can be rewritten as 15^(1/4) or √15.
• 3^1/2 is the square root of 3, which we can denote as 3^(1/2) or √3.
• We then divide the fourth root of 15 by the square root of 3.

Now we simplify:

1. (15^(1/4)) / (3^(1/2)) = (√15) / (√3)
2. Notice that 15 = 3· 5, so we can rewrite √15 as √(3· 5).
3. Since the square root function is distributive over multiplication, this becomes √3 · √5.
4. Substituting this back into the original expression: (√3 · √5) / (√3) - 2.
5. The √3 terms cancel out, leaving us with √5 - 2, which is the fourth root of 5.
6. Now we subtract 2: 5^(1/4) - 2.

Finally, we can see that 5^(1/4) is a number slightly larger than 1, so when we subtract 2, the result can't be positive, thus none of the choices provided would be correct assuming we are to evaluate the expression to find a numerical value.