Question

Sadie simplified the expression √54a^7b^3, where a>=0, as shown: √54a^7b^3= √3^2•6•a^2•a^5•b^2•b=3ab √6a^5b

Answer 1

Sadie did not factor a to the 7th power using the largest perfect power.

Instead of a squared times a to the 5th power, the factors should be a to the 6th times a to the 1st power.

In Sadie’s final answer, the exponent on a should have been 3.

Explanation:

Answer 2

We are to find the error made by Sadie and then find the correct simplification.

The error Sadie made is that she wrote
`a^7` as
`a^2 * a^5` instead of
`a^6 * a`.

The square root of
`a^6` is
`a^3` and so she could have further simplified.

The correct simplification is shown below:

`√(54a^7b^3) = √(2 * 3 * 3 * 3 * a^6 * a * b^2 * b) \\ \\= √(3^2 * a^6 * b^2 * 6 * a * b) \\\\= 3a^3b√(6ab)`