Maths-
General
Easy
Question
Rewrite expression to remove perfect square factors other than 1 in radicand. √(2x3) . √(25x2y)
Hint:
A radical expression refers to an expression containing a radical (√) symbol, commonly called as a root symbol.
A perfect square refers to a number that can be expressed as the product of an integer by itself.
We will simplify the given expressions, removing all the perfect square factors from under the radical sign.
The correct answer is: Final Answer:- ∴ The given expression can be written as 5x2 √(2xy) after removing all perfect square factors other than 1.
Step-by-step solution:-
Given expression = √(2x3) . √(25x2y)
∴ Given expression = √[2(x)3 . 25(x)2 y] …............................................... [Product property- √m × √n = √(mn)]
∴ Given expression = √(2 × 5 × 5 × x3 × x2× y) ….......................... (Factorizing the term inside the radical)
∴ Given expression = √(2 ×5 × 5 × x2+1 × x2 × y) .................................. [Product property- an × am = an+m]
∴ Given expression = √(2 × 5 × 5 × x2 × x × x2 × y) .................................. [Product property- an × am = an+m]
∴ Given expression = √2× √(5 × 5) × √(x2 × x2) × √xy …...................... [Product property- √m × √n = √(mn)]
∴ Given expression = √2 ×√(5)2 × √(x2)2 × √xy
∴ Given expression = √2 ×(5)2/2 × (x2)2/2 × √xy ............................ [Power rule- m√(bn) = b n/m]
∴ Given expression = √2 × (5)1 × (x2)1 × √xy
∴ Given expression = √2 × 5 × x2 × √xy
∴ Given expression = 5x2 ×√(2xy) …............................................... [Product property- √m × √n = √(mn)]
Final Answer:-
∴ The given expression can be written as 5x2 × √(2xy) after removing all perfect square factors other than 1.
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