jamal simplified the expression $sqrt{75x^{5}y^{8}}$ where $xgeq0$ and $ygeq0$.\n$sqrt{75x^{5}y^{8}}=sqrt{25c…

jamal simplified the expression $sqrt{75x^{5}y^{8}}$ where $xgeq0$ and $ygeq0$.\n$sqrt{75x^{5}y^{8}}=sqrt{25cdot3cdot x^{4}cdot xcdot y^{8}} = 5x^{2}y^{2}sqrt{3x}$\nwhich describes the error jamal made?\nhe should have written the square root of $y^{8}$ in the answer as $y^{4}$, not $y^{2}$.\nhe should have written the square root of $x^{4}$ in the answer as $x$, not $x^{2}$.\nhe should have written the 5 inside of the radical in the answer.\nhe should have written the 3 outside of the radical in the answer.

jamal simplified the expression $sqrt{75x^{5}y^{8}}$ where $xgeq0$ and $ygeq0$.\n$sqrt{75x^{5}y^{8}}=sqrt{25cdot3cdot x^{4}cdot xcdot y^{8}} = 5x^{2}y^{2}sqrt{3x}$\nwhich describes the error jamal made?\nhe should have written the square root of $y^{8}$ in the answer as $y^{4}$, not $y^{2}$.\nhe should have written the square root of $x^{4}$ in the answer as $x$, not $x^{2}$.\nhe should have written the 5 inside of the radical in the answer.\nhe should have written the 3 outside of the radical in the answer.

Answer

Answer:

A. He should have written the square root of $y^{8}$ in the answer as $y^{4}$, not $y^{2}$.

Explanation:

Step1: Recall square - root rule

For any non - negative real number $a$ and integer $n$, $\sqrt{a^{n}}=a^{\frac{n}{2}}$ when $n$ is even.

Step2: Analyze $\sqrt{y^{8}}$

Using the rule $\sqrt{y^{8}}$, since $n = 8$ (even), then $\sqrt{y^{8}}=y^{\frac{8}{2}}=y^{4}$, not $y^{2}$. So Jamal made an error in calculating the square root of $y^{8}$.