This question is an application of the factoring of the difference of two squares.
A^2 - b^2 = (a + b)(a - b)
You have
a = √10
b = √5
The square of a square root is the number itself.
A^2 = (√10)^2 = 10
b^2 = (√5)^2 = 5
((√10) + (√5))((√10 - (√5))
= (√10)^2 - (√5)^2
= 10 - 5
= 5
It is a good idea to memorize this factoring. It shows up a lot in algebra problems. It can actually be usefully applied to compute values in your head that might otherwise be difficult to do. This problem is an example of that.
A^2 - b^2 = (a + b)(a - b)
You have
a = √10
b = √5
The square of a square root is the number itself.
A^2 = (√10)^2 = 10
b^2 = (√5)^2 = 5
((√10) + (√5))((√10 - (√5))
= (√10)^2 - (√5)^2
= 10 - 5
= 5
It is a good idea to memorize this factoring. It shows up a lot in algebra problems. It can actually be usefully applied to compute values in your head that might otherwise be difficult to do. This problem is an example of that.
