Question
Write an expression for each product without perfect square factors in the radicand. 2√12x9 × √18x5
Hint:
A radical expression refers to an expression containing a radical (√) symbol, commonly called as a root symbol.
A radicand refers to the number that is preceded by a radical sign.
The correct answer is: The given expressions can be written using without a perfect square in the radicand as- 12x7√6.
Step-by-step solution:-
Given expression = 2√12x9 × √18x5
∴ Given expression = 2 × √(12x9 × 18x5) ..................................................................... (Product property)
∴ Given expression = 2 × √(216 × x9+5) …..................................................................... (am × an = am+n)
∴ Given expression = 2 × √(216 × x14)
∴ Given expression = 2 ×√(6 × 6 × 6 x7+7) ......................................................................... (Factorizing the given radicand)
∴ Given expression = 2 ×√(6 × 6 × 6 × x7× x7) ................................................................... (am × an = am+n)
∴ Given expression = 2 × √(6 × 6) × √6 × √(x7× x7) …................................... [Product property of radicals i.e. √m × √n = √(mn)]
∴ Given expression = 2 × √62 × √6 × √(x7)2
∴ Given expression = 2 × (6)2/2 × √6 × (x7)2/2 .................................... [Power rule- m√(bn) = b n/m]
∴ Given expression = 2 × 61 × √6 × (x7)1
∴ Given expression = 2×6 × √6 × x7
∴ Given expression = 12x7√6
Final Answer:-
∴ The given expressions can be written using without a perfect square in the radicand as- 12x7√6.
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