Question

Simplify √135+5⁢√10⁢𝑑− 3⁢√60.

Answer 1

Assuming the "d" multiplies √10 (i.e. the term is 5d√10):

√135 + 5d√10 − 3√60
= 3√15 + 5d√10 − 3(2√15) (since √135 = 3√15, √60 = 2√15)
= 3√15 + 5d√10 − 6√15
= −3√15 + 5d√10.

You can also factor out √5 if desired:
= √5(5d√2 − 3√3).