im studying radicals and im having trouble....i need help on this one....i really don't know how to write but here it goes...
the nth root is 4square root of 5 times the nth root is 4 square root of 5...i need to simplify the expression
I don't understand the expression as the text you have given.
"the nth root is 4square root of 5 times the nth root is 4 square root of 5"
Is this exactly as presented in the question you were given?
i don't know how to write it....its square root of 5 with the 4 on the left side times the square root of 5 with the 4 on the left side
OK
4sqrt5 x 4 sqrt5
another way to write this (struggling with the limits of text only!) is
5^(1/4)x5^(1/4)
(^ means to the power of so 10^2=100)
or 5 to power quarter x 5 to power quarter.
When you multiply two numbers with powers together you add the powers.
e.g. 10^2 x 10^2 = 10^4
or 100^(1/2) x 100^(1/2)=100^1 (or =100)
so
5^(1/4)x5^(1/4) =?
Does this help?
so the answer would be 5^1/2....is that right???
Yes
To simplify the expression, let's break it down step by step:
1. Start with the expression: nth root of (4√5) times nth root of (4√5).
2. Recall that when multiplying radicals with the same index (n), we can combine them by multiplying the radicands (the values inside the radical).
3. So, multiply 4√5 by 4√5:
(4√5) × (4√5) = 4 × 4 × (√5 × √5)
4. Multiply 4 by 4:
4 × 4 = 16
5. Multiply √5 by √5:
(√5 × √5) = 5
6. Now, we have 16 times 5, which equals:
16 × 5 = 80
7. Therefore, the simplified expression is 80.
In summary, the nth root of (4√5) times the nth root of (4√5) simplifies to 80.