Compare the pair of radical expressions. 2√21 & 4√5

The correct answer is: Comparing the given radicals expressions, we get- 2√21 > 4√5

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 = 2√21
∴ 1st expression = √2 × √2 × √21 ......................................... (Factorizing the term 2)
∴ 1st expression = √(2 × 2 × 21) …............................................... [Product property- √m ×√n = √(mn)]
∴ 1st expression = √84 ........................................................ (Equation i)
2nd expression = 4√5
∴ 2nd expression = √4 × √4 × √5 ......................................... (Factorizing the term 4)
∴ 2nd expression = √(4 × 4 × 5) …............................................... [Product property- √m × √n = √(mn)]
∴ 2nd expression = √80 ........................................................ (Equation ii)
Comparing Equations i & ii, we get-
√84 > √80
Hence, 2√21 > 4√5
Final Answer:-
∴ Comparing the given radicals expressions, we get- 2√21 > 4√5.