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The quotient equivalent to the expression [tex]\sqrt{50x^3} \div \sqrt{32x^2}[/tex] is (5√x)/4.
Hence option B is the right choice.
To find the quotient of an expression, we simplify the numerators and the denominators and then cancel off the like terms.
In the question, we are asked to find the equivalent expression to the quotient given by [tex]\sqrt{50x^3} \div \sqrt{32x^2}[/tex] .
To find the equivalent expression, we need to simplify the given quotient as follows:
{√(50x³)}/{√(32x²)}
= {√(25.2.x².x)}/{√(16.2.x²)} [Since, 50x³ = 25.2.x².x, and 32x² = 16.2.x²]
= {√(5².2.x².x)}/{√(4².2.x²)} [Since, 25 = 5², and 16 = 4²]
= (5x.√2.√x)/(4x√2) [Since, √(ab) = √a√b, and √a² = a]
= (5√x)/4 [Cancelling the like terms √2 and x].
Thus, the equivalent expression is (5√x)/4.
Thus, the quotient equivalent to the expression [tex]\sqrt{50x^3} \div \sqrt{32x^2}[/tex] is (5√x)/4. Hence option B is the right choice.
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