Can you explain to me, in the simplest terms possible, how to solve 3√8 - √18 + 3√72 - √75?

Question

Explain this to me how you'd explain it to a five-year-old who isn't quite a prodigy but isn't completely mentally deficient, either. It'd be greatly appreciated.

Answer 1

The key is to find perfect squares in the expression under each radical.  The first 6 perfect squares are:

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

 

3√8 - √18 + 3√72 - √75

 

= 3√(4·2) - √(9·2) + 3√(36·2) - √(25·3)

 

= 3√(2²·2) - √(3²·2) + 3√(6²·2) - √(5²·3)

 

= 3·2√2 - 3√2 + 3·6√2 - 5√3                   [NOTE:  √(a²) = a]

 

= 6√2 - 3√2 + 18√2 - 5√3

 

Now, you can add/subtract the terms with the same term under the radical:

 

= 21√2 + 5√3