Question

Sadie simplified the expression StartRoot 54 a Superscript 7 b cubed EndRoot, where a greater-than-or-equal-to 0, as shown colon StartRoot 54 a Superscript 7 baseline b cubed EndRoot = StartRoot 3 squared times 6 times a squared times a Superscript 5 Baseline times b squared times b EndRoot = 3 a b StartRoot 6 a Superscript 5 Baseline b EndRoot Describe the error Sadie made, and explain how to find the correct answer.\

Answer 1

Answer:

Sadie's error is " she made error in step 2 $=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$  where $a\geqslant 0$"

Because she made error in splitting the powers to simplify the square root

Therefore the correct answer for Sadie's expression is $3ab\sqrt{6ab}$ where $a\geqslant 0$

Step-by-step explanation:

Given that " Sadie simplified the expression StartRoot 54 a Superscript 7 b cubed EndRoot, where a greater-than-or-equal-to 0, "

It can be written as $\sqrt{54a^7b^3}$ where $a\geqslant 0$

The given expression is $\sqrt{54a^7b^3}$ where $a\geqslant 0$

To find Sadie's error and explain the correct answer :

Sadie's steps are

$\sqrt{54a^7b^3}$  where $a\geqslant 0$

$=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$

$=3ab\sqrt{6a^5b}$

$\sqrt{54a^7b^3}=3ab\sqrt{6a^5b}$ where $a\geqslant 0$

Now corrected steps are

$\sqrt{54a^7b^3}$  where $a≥0$

$=\sqrt{(9\times 6)(a^{6+1})(b^{2+1})$

$=\sqrt{(3^2\times 6)(a^6.a^1)(b^2.b^1)$ (by using the identity $a^{m+n}=a^m.a^n$

$=\sqrt{3^2\times 6\times ((a^3)^2.a)(b^2.b)$ (by using the identity $a^{mn}=(a^m)^n$ )

$=3ab\sqrt{6ab}$

Therefore $\sqrt{54a^7b^3}=3ab\sqrt{6ab}$  where $a\geqslant 0$

The correct answer is $3ab\sqrt{6ab}$ where $a\geqslant 0$

Sadie's error is " she made error in step 2 $=\sqrt{3^2\times 6\times a^2\times a^5\times b^2\times b}$ " where $a\geqslant 0$

Because she made error in splitting the powers to simplify the square root

Therefore the correct answer for Sadie's expression is $3ab\sqrt{6ab}$ where $a\geqslant 0$

Answer 2

Answer:

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.

Step-by-step explanation: EDGE 2021:)