Question

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

Step 1: Explain the error made

Step 2: Explain how to find the correct answer.

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:


`√(54a^7b^3)=√(3^2\cdot 6\cdot a^2\cdot a^5\cdot b^2\cdot b) =3\cdot a\cdot |b| √(6\cdot a^5\cdot b)=3ab√(6a^5b)`.

3. The simpliest expression is
`3ab√(6a^5b) =3ab√(6\cdot a^2\cdot a^2\cdot a\cdot b) =3a^3b√(6ab)`.