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

Answer:

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:

$\sqrt{54a^7b^3} = \sqrt{2 * 3 * 3 * 3 * a^6 * a * b^2 * b} \\ \\= \sqrt{3^2 * a^6 * b^2 * 6 * a * b} \\\\= 3a^3b\sqrt{6ab}$