Please help! Can you multiply different numbers with different roots? such as the 4th root of 2 times square root of 3
yes 16 x 9 = 144
samantha you must have confused my roots for powers.. it is not 2 to the 4th power it is the 4th root of 2 and same the square root of 3 not 3 squared... but thanks for trying
Sam, answer me this:
Could you multiply (x^3)(y^4) ?
(2^(1/4))(√3) is the same sort of thing.
To multiply powers, they must have either the same base or the same exponent
e.g. (x^5)(x^4) = x^9
(x^5)(y^5) = (xy)^5
Yes, you can multiply different numbers with different roots. To multiply these numbers, you need to simplify each root separately and then multiply the simplified values.
Let's take the example you provided: the 4th root of 2 multiplied by the square root of 3.
Step 1: Simplify each root separately.
- The 4th root of 2 means finding a number that, when raised to the power of 4, equals 2. In this case, 2^(1/4) is the 4th root of 2.
- The square root of 3 is the number that, when multiplied by itself, gives 3. So, √3 is the square root of 3.
Step 2: Multiply the simplified values.
- Multiply 2^(1/4) (the 4th root of 2) by √3 (the square root of 3).
- Final result: 2^(1/4) * √3.
Alternatively, you can express both roots using exponents and rewrite the multiplication:
2^(1/4) * √3 = 2^(1/4) * 3^(1/2).
Now, both terms have the same base (2), so you can combine the exponents:
2^(1/4) * 3^(1/2) = 2^(1/4 + 1/2).
Simplifying further:
2^(1/4 + 1/2) = 2^(1/4 + 2/4) = 2^(3/4).
So, the final answer is 2^(3/4).
Note that this is the most simplified form of the expression, but you can further evaluate it or approximate it numerically if needed.