Compare the pair of radical expressions. 1/2√120 & √30

The correct answer is: Comparing the given radicals expressions, we get- 1/2√120 = √30

Hint:-
A radical expression refers to an expression containing a radical (√) symbol, commonly called as a root symbol.
We will simplify the given expressions and compare the same with each other.
"Step-by-step solution:-
1st expression = 1/2√120
∴ 1st expression = 1/2 × √(2 ×2 × 2 × 5 × 3) ......................................... (Factorizing the term 12)
∴ 1st expression = 1/2 × √(2 × 2) × √(2 × 5 × 3) …............................................... [Product property- √m ×  √n = √(mn)]
∴ 1st expression = 1/2 × √22 ×  √(2 ×5 ×  3)
∴ 1st expression = 1/2 × 22/2 × √(2 × 5 × 3) ........................................................ [Power rule- m√(bn) = b n/m]
∴ 1st expression = 1/2 × 21 × √30
∴ 1st expression = 1 × √30
∴ 1st expression = √30 ........................................................ (Equation i)
2nd expression = √30 ........................................................ (Equation ii)
Comparing Equations i & ii, we get-
√30 = √30
Hence, 1/2√120 = √30
Final Answer:-
∴ Comparing the given radicals expressions, we get- 1/2√120 = √30.