Answer:
53 sqrt(2)
Explanation:
Hi Addisonrausch, how are you?
In this exercise you must simplify the roots and then be able to solve the equation.
Next step by step:
The first is to simplify the roots. To do this, always try dividing the radicand by one of the prime numbers: 2, 3, 5, 7, 9, etc. If the number is even (as in this exercise you have both numbers 200 and 162 are even) tests dividing by 2 and expressing that number as the multiplication of 2 by the result number.
8 sqrt (100 * 2) - 3 sqrt (81 * 2)
Then you can express the number 100 as the square of 10 (since 10 ^ 2 = 10 * 10 = 100). Similarly, you can express 81 as the square of 9 (9 ^ 2 = 9 * 9 = 81).
8 sqrt ((10 ^ 2) * 2) - 3 sqrt ((9 ^ 2) * 2)
Then, you distribute the square root between the factors (this is a property of the powers and roots).
8 (sqrt (10 ^ 2) * sqrt (2)) - 3 (sqrt (9 ^ 2) * sqrt (2))
You simplify the power squared with the square root
8 * 10 sqrt (2) - 3 * 9 sqrt (2)
80 sqrt (2) - 27 sqrt (2)
By having the square root subtracted you can proceed with the subtraction:
(80-27) sqrt (2)
53 sqrt (2)
Ready!
I hope I've been helpful!
Regards