Question

3 simplify assume that all variables are greater than or equal to zero
(sqrt4{\frac{43x^4}{81}})
(sqrt4{\frac{43x^4}{81}} = square)
(type an exact answer, using radicals as needed. simplify your answer.)

Explanation:

Step1: Simplify the fraction inside the square root

First, we simplify the fraction \(\frac{43x^4}{81}\). We can separate the square root of a fraction into the fraction of square roots: \(\sqrt{\frac{43x^4}{81}}=\frac{\sqrt{43x^4}}{\sqrt{81}}\)

Step2: Simplify the square roots of the numerator and the denominator

We know that \(\sqrt{81} = 9\) and \(\sqrt{x^4}=x^2\) (since \(x\geq0\)). So \(\sqrt{43x^4}=\sqrt{43}\cdot\sqrt{x^4}=\sqrt{43}x^2\)
Then we have \(\frac{\sqrt{43}x^2}{9}\)

Answer:

\(\frac{x^{2}\sqrt{43}}{9}\)