rewritten as a power of 2 with a rational exponent, the expression
4*squared root of 2 would equal which of the following.
1) 2 so 2 is just 2
2)2^2 which would =4
3) 2^5/2 this =5.65
4)2^5 this=32
4*square root of two=5.65
so I believe the answer is 3. Is that correct? Thanks for checking my work.
4 * sqrt ( 2 ) =
sqrt ( 16 ) * sqrt ( 2 ) =
sqrt ( 32 ) =
sqrt ( 2 ^ 5 ) =
( 2 ^ 5 ) ^ ( 1 / 2 ) =
2 ^ ( 5 / 2 )
Answer 3
It is not 4 squared times 2 the equation
It is 4 times the square root of two.
so my second step was to first get the square root of 2, which=1.4142
the multiplied it by 4
s0 4 x 1.412=5.65
Am I correct?
sqrt mean :
square root
4 * sqrt ( 2 ) = 4 * square root of 2
ANSWER 3
To rewrite an expression as a power of 2 with a rational exponent, you can use the properties of exponents.
In this case, the expression is 4 * square root of 2. Let's break it down step by step:
Step 1: Rewrite the square root of 2 as a power of 2. The square root of 2 can be expressed as 2^(1/2).
Step 2: Apply the exponent to the entire expression. So, 4 * square root of 2 is equivalent to 4 * (2^(1/2)).
Step 3: Use the property of exponents that states when you multiply two numbers with the same base, you can add their exponents. So, 4 * (2^(1/2)) is equivalent to (4 * 2)^(1/2) = 8^(1/2).
Step 4: The exponent 1/2 means square root. So, 8^(1/2) is equivalent to the square root of 8.
Now, let's compare the options:
1) 2 - This is just 2, not equal to the expression.
2) 2^2 - This is equal to 4, not equal to the expression.
3) 2^(5/2) - This is equal to 5.65, which is the same as the expression 4 * square root of 2.
4) 2^5 - This is equal to 32, not equal to the expression.
Therefore, the correct answer is option 3) 2^(5/2), which is equal to 5.65.
Well done! Your work is correct.