Math / Algebra

Questionc) $\frac{\sqrt{28} \sqrt{4}}{\sqrt{7}}$

Studdy Solution

STEP 1

What is this asking? Simplify this expression with square roots and multiplication. Watch out! Don't forget to simplify the roots as much as possible!

STEP 2

1. Simplify the square roots
2. Multiply the numerators
3. Simplify the fraction

STEP 3

Alright, let's break down these square roots!
We've got $\sqrt{28}$ , $\sqrt{4}$ , and $\sqrt{7}$ .
We want to simplify them as much as possible before we do anything else.

STEP 4

Let's start with $\sqrt{28}$ .
We can rewrite $28$ as $4 \cdot 7$ , so $\sqrt{28}$ becomes $\sqrt{4 \cdot 7}$ .
Since $\sqrt{4}$ is just $2$ , we can simplify this to $2\sqrt{7}$ .
Awesome!

STEP 5

Next up is $\sqrt{4}$ .
This one's easy!
It's just $2$ .

STEP 6

Finally, we have $\sqrt{7}$ .
This one can't be simplified any further, so we'll leave it as $\sqrt{7}$ .

STEP 7

Now, let's multiply the top part of our fraction.
We have $2\sqrt{7} \cdot 2$ , which simplifies to $4\sqrt{7}$ .

STEP 8

Now we have $\frac{4\sqrt{7}}{\sqrt{7}}$ .
We can divide the top and bottom by $\sqrt{7}$ .
Remember, anything divided by itself is $1$ , so $\frac{\sqrt{7}}{\sqrt{7}} = 1$ .

STEP 9

So, we're left with $4 \cdot 1$ , which is just $4$ !

STEP 10

Our final answer is $4$ !

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Questionc) $\frac{\sqrt{28} \sqrt{4}}{\sqrt{7}}$

Studdy Solution

STEP 1

What is this asking? Simplify this expression with square roots and multiplication. Watch out! Don't forget to simplify the roots as much as possible!

STEP 2

1. Simplify the square roots
2. Multiply the numerators
3. Simplify the fraction

STEP 3

Alright, let's break down these square roots!
We've got $\sqrt{28}$ , $\sqrt{4}$ , and $\sqrt{7}$ .
We want to simplify them as much as possible before we do anything else.

STEP 4

Let's start with $\sqrt{28}$ .
We can rewrite $28$ as $4 \cdot 7$ , so $\sqrt{28}$ becomes $\sqrt{4 \cdot 7}$ .
Since $\sqrt{4}$ is just $2$ , we can simplify this to $2\sqrt{7}$ .
Awesome!

STEP 5

Next up is $\sqrt{4}$ .
This one's easy!
It's just $2$ .

STEP 6

Finally, we have $\sqrt{7}$ .
This one can't be simplified any further, so we'll leave it as $\sqrt{7}$ .

STEP 7

Now, let's multiply the top part of our fraction.
We have $2\sqrt{7} \cdot 2$ , which simplifies to $4\sqrt{7}$ .

STEP 8

Now we have $\frac{4\sqrt{7}}{\sqrt{7}}$ .
We can divide the top and bottom by $\sqrt{7}$ .
Remember, anything divided by itself is $1$ , so $\frac{\sqrt{7}}{\sqrt{7}} = 1$ .

STEP 9

So, we're left with $4 \cdot 1$ , which is just $4$ !

STEP 10

Our final answer is $4$ !

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Questionc) 2847\frac{\sqrt{28} \sqrt{4}}{\sqrt{7}}7​28​4​​

Studdy Solution

STEP 1

What is this asking? Simplify this expression with square roots and multiplication. Watch out! Don't forget to simplify the roots as much as possible!

STEP 2

1. Simplify the square roots2. Multiply the numerators3. Simplify the fraction

STEP 3

Alright, let's **break down** these square roots!We've got 28\sqrt{28}28​, 4\sqrt{4}4​, and 7\sqrt{7}7​.We want to simplify them as much as possible before we do anything else.

STEP 4

Let's start with 28\sqrt{28}28​.We can rewrite 282828 as 4⋅74 \cdot 74⋅7, so 28\sqrt{28}28​ becomes 4⋅7\sqrt{4 \cdot 7}4⋅7​.Since 4\sqrt{4}4​ is just 222, we can simplify this to 272\sqrt{7}27​.Awesome!

STEP 5

Next up is 4\sqrt{4}4​.This one's easy!It's just 222.

STEP 6

Finally, we have 7\sqrt{7}7​.This one can't be simplified any further, so we'll leave it as 7\sqrt{7}7​.

STEP 7

Now, let's **multiply** the **top** part of our fraction.We have 27⋅22\sqrt{7} \cdot 227​⋅2, which simplifies to 474\sqrt{7}47​.

STEP 8

Now we have 477\frac{4\sqrt{7}}{\sqrt{7}}7​47​​.We can **divide** the **top** and **bottom** by 7\sqrt{7}7​.Remember, anything divided by itself is 111, so 77=1\frac{\sqrt{7}}{\sqrt{7}} = 17​7​​=1.

STEP 9

So, we're left with 4⋅14 \cdot 14⋅1, which is just 444!

STEP 10

Our **final answer** is 444!

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Questionc) $\frac{\sqrt{28} \sqrt{4}}{\sqrt{7}}$

1. Simplify the square roots
2. Multiply the numerators
3. Simplify the fraction

Alright, let's break down these square roots!
We've got $\sqrt{28}$ , $\sqrt{4}$ , and $\sqrt{7}$ .
We want to simplify them as much as possible before we do anything else.

Let's start with $\sqrt{28}$ .
We can rewrite $28$ as $4 \cdot 7$ , so $\sqrt{28}$ becomes $\sqrt{4 \cdot 7}$ .
Since $\sqrt{4}$ is just $2$ , we can simplify this to $2\sqrt{7}$ .
Awesome!

Next up is $\sqrt{4}$ .
This one's easy!
It's just $2$ .

Finally, we have $\sqrt{7}$ .
This one can't be simplified any further, so we'll leave it as $\sqrt{7}$ .

Now, let's multiply the top part of our fraction.
We have $2\sqrt{7} \cdot 2$ , which simplifies to $4\sqrt{7}$ .

Now we have $\frac{4\sqrt{7}}{\sqrt{7}}$ .
We can divide the top and bottom by $\sqrt{7}$ .
Remember, anything divided by itself is $1$ , so $\frac{\sqrt{7}}{\sqrt{7}} = 1$ .

So, we're left with $4 \cdot 1$ , which is just $4$ !

Our final answer is $4$ !