Given x 0 and y 0, select the expression that is equivalent to sqrt(-36x^(4)y^(9)) -6x^(2)y^((9)/(2)) 6ix^((1)/(2))y^((2)/(9)) -6x^((1)/(2))y^((2)/(9)) 6ix^(2)y^((9)/(2))

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  sqrt(-36x^(4)y^(9))  -6x^(2)y^((9)/(2))  6ix^((1)/(2))y^((2)/(9))  -6x^((1)/(2))y^((2)/(9))  6ix^(2)y^((9)/(2))

Bytelearn · Accepted Answer

Recognize Imaginary Unit i: First, we need to recognize that the square root of a negative number involves the imaginary unit i, where i^2 = -1. Therefore, sqrt(-1) = i.Rewrite Expression by Factoring: Next, we can rewrite the expression inside the square root by factoring out -1 from -36, which will be taken care of by the imaginary unit i when we take the square root. So, sqrt(-36x^(4)y^(9)) = sqrt(-1) * sqrt(36x^(4)y^(9)).Take Square Root Separately: Now, we can take the square root of -1 as i and the square root of 36x^(4)y^(9) separately. The square root of 36 is 6, the square root of x^(4) is x^(2) (since x > 0), and the square root of y^(9) is y^((9)/(2)) (since y > 0).Multiply Simplified Expression: Multiplying these together, we get the expression: i * 6 * x^(2) * y^((9)/(2)). This simplifies to 6ix^(2)y^((9)/(2)).Compare with Given Options: Comparing the simplified expression with the given options, we find that 6ix^(2)y^((9)/(2)) matches one of the options exactly.

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt{-36 x^{4} y^{9}}$ $\newline$ $-6 x^{2} y^{\frac{9}{2}}$ $\newline$ $6 i x^{\frac{1}{2}} y^{\frac{2}{9}}$ $\newline$ $-6 x^{\frac{1}{2}} y^{\frac{2}{9}}$ $\newline$ $6 i x^{2} y^{\frac{9}{2}}$

Full solution

More problems from Find derivatives of using multiple formulae

Related topics