Question

Describe the error Sadie made, and explain how to find the correct answer. (Refer to image)

Answer 1

Sadie said that 54=3^3*6, which is false bacause 54=3^2*6. that's why she was wrong
radical 54a^7b^3=radical 3^2*6*a^6*a*b^2*b=3a^3b radical 6ab

Answer 2

1. Sadie should note that $54a^7b^3\ge 0$ and if $a\ge 0$, then $b\ge 0$.

2. While simplifying Sadie makes some mistakes (it must be $3^2$ instead of $3^3$ and she missed the sign of absolute value for b). The right way to find the correct answer is:

$\sqrt{54a^7b^3}=\sqrt{3^2\cdot 6\cdot a^2\cdot a^5\cdot b^2\cdot b} =3\cdot a\cdot |b| \sqrt{6\cdot a^5\cdot b}=3ab\sqrt{6a^5b}$.

3. The simpliest expression is $3ab\sqrt{6a^5b} =3ab\sqrt{6\cdot a^2\cdot a^2\cdot a\cdot b} =3a^3b\sqrt{6ab}$.