Math / Algebra

QuestionEllot is Simplifying a radical. His work is shown. $\begin{array}{l} \sqrt{64}=\sqrt{4 \cdot 16} \\ \sqrt{4 \cdot 16}=2 \sqrt{16} \\ \sqrt{64}=2 \sqrt{16} \end{array}$
Which statement best applies to Eliot's mathematical work? The equality $\sqrt{64}=\sqrt{4 \cdot 16}$ is incorrect or invalid. Removing the 4 from under the radical in the second step is incorrect or invalid. The work shown above is correct; however. $2 \sqrt{26}$ may be simplified further. The work shown above is correct, and $2 \sqrt{16}$ may not be simplified further-

Studdy Solution

STEP 1

What is this asking? Is Eliot correctly simplifying $\sqrt{64}$ , and if so, can his result be simplified further? Watch out! Remember that simplifying a radical means expressing it in its simplest form, which might involve taking perfect squares out from under the radical.

STEP 2

1. Analyze Eliot's first step.
2. Analyze Eliot's second step.
3. Analyze Eliot's final result.

STEP 3

Eliot starts with $\sqrt{64}$ and rewrites it as $\sqrt{4 \cdot 16}$ .
This is perfectly valid!
Since $4 \cdot 16 = 64$ , replacing $\sqrt{64}$ with $\sqrt{4 \cdot 16}$ is just like replacing $2$ with $1+1$ .
It's the same value, just written differently!

STEP 4

Eliot takes $\sqrt{4 \cdot 16}$ and simplifies it to $2\sqrt{16}$ .
This is also correct!
Remember that $\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}$ .
So, $\sqrt{4 \cdot 16}$ can be rewritten as $\sqrt{4} \cdot \sqrt{16}$ .
Since $\sqrt{4} = 2$ , we get $2 \cdot \sqrt{16}$ , or just $2\sqrt{16}$ .
Great work so far, Eliot!

STEP 5

Eliot's current result is $2\sqrt{16}$ .
Can this be simplified further?
Absolutely! Notice that $16$ is a perfect square.
We know that $\sqrt{16} = 4$ .
So, $2\sqrt{16}$ becomes $2 \cdot 4$ , which is $8$ .
And guess what? $\sqrt{64}$ is indeed $8$ !

STEP 6

The work shown is correct so far, however, $2\sqrt{16}$ may be simplified further.

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Studdy Solution

STEP 1

What is this asking? Is Eliot correctly simplifying $\sqrt{64}$ , and if so, can his result be simplified further? Watch out! Remember that simplifying a radical means expressing it in its simplest form, which might involve taking perfect squares out from under the radical.

STEP 2

1. Analyze Eliot's first step.
2. Analyze Eliot's second step.
3. Analyze Eliot's final result.

STEP 3

Eliot starts with $\sqrt{64}$ and rewrites it as $\sqrt{4 \cdot 16}$ .
This is perfectly valid!
Since $4 \cdot 16 = 64$ , replacing $\sqrt{64}$ with $\sqrt{4 \cdot 16}$ is just like replacing $2$ with $1+1$ .
It's the same value, just written differently!

STEP 4

STEP 5

Eliot's current result is $2\sqrt{16}$ .
Can this be simplified further?
Absolutely! Notice that $16$ is a perfect square.
We know that $\sqrt{16} = 4$ .
So, $2\sqrt{16}$ becomes $2 \cdot 4$ , which is $8$ .
And guess what? $\sqrt{64}$ is indeed $8$ !

STEP 6

The work shown is correct so far, however, $2\sqrt{16}$ may be simplified further.

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Studdy Solution

STEP 1

What is this asking? Is Eliot correctly simplifying 64\sqrt{64}64​, and if so, can his result be simplified further? Watch out! Remember that simplifying a radical means expressing it in its simplest form, which might involve taking perfect squares out from under the radical.

STEP 2

1. Analyze Eliot's first step.2. Analyze Eliot's second step.3. Analyze Eliot's final result.

STEP 3

STEP 4

STEP 5

Eliot's current result is 2162\sqrt{16}216​.Can this be simplified further?Absolutely! Notice that 161616 is a perfect square.We know that 16=4\sqrt{16} = 416​=4.So, 2162\sqrt{16}216​ becomes 2⋅42 \cdot 42⋅4, which is 888.And guess what? 64\sqrt{64}64​ is indeed 888!

STEP 6

The work shown is correct so far, however, 2162\sqrt{16}216​ may be simplified further.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Is Eliot correctly simplifying $\sqrt{64}$ , and if so, can his result be simplified further? Watch out! Remember that simplifying a radical means expressing it in its simplest form, which might involve taking perfect squares out from under the radical.

1. Analyze Eliot's first step.
2. Analyze Eliot's second step.
3. Analyze Eliot's final result.

Eliot's current result is $2\sqrt{16}$ .
Can this be simplified further?
Absolutely! Notice that $16$ is a perfect square.
We know that $\sqrt{16} = 4$ .
So, $2\sqrt{16}$ becomes $2 \cdot 4$ , which is $8$ .
And guess what? $\sqrt{64}$ is indeed $8$ !

The work shown is correct so far, however, $2\sqrt{16}$ may be simplified further.