Can someone explain the details for calculating roots?In the following problem the # in the () is the s. root.

Question

2(8)*6(9)

4(2)*6(9)

24(18)

answer: 72(2)

Answer 1

2sqrt(8) * 6sqrt(9)
2sqrt(4 * 2) * 18
4sqrt(2) * 18
72sqrt(2)

lets take what you had

24sqrt(18)
24sqrt(9 * 2)
72sqrt(2)

or to make it easier to understand

24sqrt(18)
24sqrt(9 * 2)
24 * sqrt(9) * sqrt(2)
24 * 3 * sqrt(2)
(24 * 3)sqrt(2)
72sqrt(2)

Answer 2

First :
* (a) *(b) = (a*b)
* K (a) * L (b) = K * L * (a*b)
Second : to simplify the s. root you analyze the number to its simplest factors, every twice similar factors come out the root, just like
(72) =( 2 * 2 * 2 * 3 * 3) = 2*3*(2)
In yours, 4(2)*6(9) = 24 (18) = 24 ( 2*3*3) = 24*3 *(2)=72(2)

Answer 3

2 (8) X 6 (9)

2 X(4 x 2) x 6 X 3 as 3= (9)
2X (4) X (2) X6 X3 (8) can be written as (4) X (2)

2X2 X (2) X 6 X 3 as 2 = (4)

2x2x6X3 (2)
as 2x2x6x3 = 72
72(2)

Answer 4

There are some methods or algorithms. Repeated division and Babylon are two.