simplify (^4 square root of 64)
Would it be (^2 square root of 4) or (^2 sqyare root of 2)?
Your phrasing does not make sense but I am guessing that you meant the fourth root of 64 or 64^(1/4)
64 = 8*8 = 4*2*4*2 = 4^3 = 2^6
2^6 = 2^4*2^2
so
(2^6)^(1/4) = 2^(4/4)*2^(2/4)
which is 2 sqrt 2
or alternatively
(2^6)^(1/4) =2^(6/4) = 2^(3/2)=sqrt(8) = 2 sqrt2
Why did the square root go to the circus? Because it wanted to be a square dancer! Now, let's simplify the expression. The fourth power of the square root of 64 can be written as the square root of 64 raised to the fourth power, which is simply 64. So the answer is 64. No complicated square dancing here!
To simplify the expression (^4 square root of 64), we can break it down step-by-step:
Step 1: Start by simplifying the square root of 64.
Since the square root of 64 is 8, the expression becomes (^4 8).
Step 2: Next, apply the exponent of 4 to 8.
To simplify (^4 8), we raise 8 to the power of 4.
8^4 = 8 × 8 × 8 × 8 = 4,096.
Therefore, (^4 square root of 64) simplifies to 4,096.
To simplify the expression ^4√64, we want to find the value that, when raised to the 4th power, equals 64. In other words, we need to find a number x, such that x^4 = 64.
To find this value, we can start by listing some perfect squares and their roots:
1^2 = 1
2^2 = 4
3^2 = 9
4^2 = 16
5^2 = 25
6^2 = 36
7^2 = 49
8^2 = 64
9^2 = 81
10^2 = 100
From this list, we can see that the square root of 64 is 8, because 8^2 = 64.
Now that we've found the square root of 64, we can simplify the expression (^4√64) as follows:
(^4√64) = (^4√(8^2))
Since (^4√(a^b)) = (a^b/4), we can rewrite the expression as:
(^4√(8^2)) = (8^(2/4))
The exponent 2/4 simplifies to 1/2, so the final answer is:
(^4√64) = 8^(1/2)
Therefore, the simplified expression is (^2√8) or (^2√(2^3)).