5sqrt8T (x) sqrt32T^5
To simplify the expression 5√8T * √32T^5, you can follow these steps:
Step 1: Simplify the values inside the square roots.
Let's simplify the square roots separately:
√8 can be split into √(4 * 2).
Since √4 = 2, we can write it as 2√2.
√32 can be split into √(16 * 2).
Since √16 = 4, we can write it as 4√2.
Now, the expression becomes:
5 * 2√2T * 4√2T^5.
Step 2: Multiply the numerical values.
5 * 2 * 4 gives us 40.
Now we have:
40√2T * √2T^5.
Step 3: Multiply the variables.
For the variable T, we add the exponents:
T * T^5 = T^(1+5) = T^6.
Now we have:
40√2T^6 * √2.
Step 4: Multiply the square roots.
When multiplying square roots, we multiply the numbers inside and the square root itself:
√2 * √2 = 2.
Finally, we have:
40 * 2 * √2T^6 = 80√2T^6.
Therefore, the simplified expression is 80√2T^6.