squareroot of 8 * exponents 3
If you mean √8^3 that's just
√8*√8*√8 = √512 = √(256*2) = √256*√2 = 16√2
or,
(2√2)^3 = 2^3*√2^3 = 8*2√2 = 16√2
sqrt ( 8 ) ^ 3 = sqrt ( 8 ) * sqrt ( 8 ) * sqrt ( 8 ) =
sqrt ( 8 ) ^ 2 * sqrt ( 8 ) = 8 * sqrt ( 8 ) = 8 * sqrt ( 4 * 2 ) =
8 * sqrt ( 4 ) * sqrt ( 2 ) = 8 * 2 * sqrt ( 2 ) = 16 * sqrt ( 2 )
To calculate the square root of 8, follow these steps:
Step 1: Determine the prime factors of 8. The prime factors of 8 are 2 x 2 x 2, or 2³.
Step 2: Group the prime factors in pairs, taking one factor from each pair. In this case, we have one pair: 2 x 2.
Step 3: Take one factor from each pair and multiply them together. In this case, you multiply 2 x 2, which equals 4.
Therefore, the square root of 8 is 2√2, or simply 2 times the square root of 2.
Now, if you want to multiply this result by the exponent of 3, you would simply raise it to the power of 3, or cube it.
(2√2)³ = (2³) √(2³)
Simplifying further:
(2³) = 8
Therefore,
(2√2)³ = 8√(2³)
Now, we have the cube of 8 multiplied by the square root of 2 cubed, which is:
8√(2³) = 8√8
You could simplify this further by breaking down 8 into 2 x 2 x 2, just like we did before:
8√8 = 8√(2 x 2 x 2)
Taking one factor of 2 from each pair:
8√(2 x 2 x 2) = 8 x (2√2)
Finally, you get:
8 x (2√2) = 16√2
So, the result of the square root of 8 multiplied by the exponent of 3 is 16√2.