To simplify the expression √2 × ∛2, we can start by expressing both roots in exponent form.
The square root of 2 can be written as 2^(1/2) and the cube root of 2 as 2^(1/3). Therefore, the expression becomes:
2^(1/2) × 2^(1/3)
When multiplying numbers with the same base, we can add the exponents:
2^(1/2 + 1/3)
To add the fractions 1/2 and 1/3, we need a common denominator. The least common multiple of 2 and 3 is 6. We can convert the fractions:
- 1/2 = 3/6
- 1/3 = 2/6
Now we can add them:
3/6 + 2/6 = 5/6
So, we have:
2^(5/6)
This simplifies our original expression to:
√2 × ∛2 = 2^(5/6)
Thus, the simplified form of the square root of 2 multiplied by the cube root of 2 is 2^(5/6).