Finding the Integer Closest to the Cube Root of the Square Root of 2
The expression in the image is asking for the cube root of the square root of 2, written as ∛√2. This can also be written as 2^(1/3 * 1/2), which simplifies to 2^(1/6).
Now, to find the integer closest to 2^(1/6), we can try to estimate this value. Since 2^(1/6) is the sixth root of 2, we're looking for a number which, when raised to the power of 6, is closest to 2.
Starting with 1, we see that 1^6 = 1, which is far from 2. Next, let's take 2^6, which is 64; this is much larger than 2. Therefore, the integer closest to 2^(1/6) must be 1, since any number greater than 1 raised to the power of 6 will be greater than 2.
So, the integer closest to ∛√2 is 1.
