Math / Algebra

QuestionSimplify $10 \sqrt{2 y}+5 \sqrt{2 y}+3 \sqrt{2 y}$ . $18 \sqrt{6 y}$ $18 \sqrt{2 y}$ $12 \sqrt{2 y}$ $18 \sqrt{6 y^{3}}$

Studdy Solution

STEP 1

What is this asking? We're asked to combine like terms involving square roots.
It's like adding apples together! Watch out! Don't multiply the numbers inside the square roots!
We're adding, not multiplying.

STEP 2

1. Identify Like Terms
2. Combine Coefficients
3. Simplify the Expression

STEP 3

Alright, let's look at what we've got!
We have $10\sqrt{2y}$ , $5\sqrt{2y}$ , and $3\sqrt{2y}$ .
Notice how they all have the same radical part, $\sqrt{2y}$ .
That's super important because it means they're like terms, just like $10x$ , $5x$ , and $3x$ are like terms.

STEP 4

Since our terms are like terms, we can add their coefficients together.
The coefficients are the numbers in front of the radical.
So, we have $10 + 5 + 3$ .

STEP 5

Let's do the addition: $10 + 5 + 3 = 18$ . Boom!

STEP 6

Now, we just put it all together.
We have $\mathbf{18}$ as our combined coefficient, and the radical part stays the same, $\sqrt{2y}$ .

STEP 7

So, our simplified expression is $18\sqrt{2y}$ !
We just added the coefficients and kept the radical part unchanged.
It's like adding 10 apples + 5 apples + 3 apples = 18 apples!

STEP 8

The simplified expression is $18\sqrt{2y}$ .

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QuestionSimplify $10 \sqrt{2 y}+5 \sqrt{2 y}+3 \sqrt{2 y}$ . $18 \sqrt{6 y}$ $18 \sqrt{2 y}$ $12 \sqrt{2 y}$ $18 \sqrt{6 y^{3}}$

Studdy Solution

STEP 1

What is this asking? We're asked to combine like terms involving square roots.
It's like adding apples together! Watch out! Don't multiply the numbers inside the square roots!
We're adding, not multiplying.

STEP 2

1. Identify Like Terms
2. Combine Coefficients
3. Simplify the Expression

STEP 3

Alright, let's look at what we've got!
We have $10\sqrt{2y}$ , $5\sqrt{2y}$ , and $3\sqrt{2y}$ .
Notice how they all have the same radical part, $\sqrt{2y}$ .
That's super important because it means they're like terms, just like $10x$ , $5x$ , and $3x$ are like terms.

STEP 4

Since our terms are like terms, we can add their coefficients together.
The coefficients are the numbers in front of the radical.
So, we have $10 + 5 + 3$ .

STEP 5

Let's do the addition: $10 + 5 + 3 = 18$ . Boom!

STEP 6

Now, we just put it all together.
We have $\mathbf{18}$ as our combined coefficient, and the radical part stays the same, $\sqrt{2y}$ .

STEP 7

So, our simplified expression is $18\sqrt{2y}$ !
We just added the coefficients and kept the radical part unchanged.
It's like adding 10 apples + 5 apples + 3 apples = 18 apples!

STEP 8

The simplified expression is $18\sqrt{2y}$ .

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QuestionSimplify 102y+52y+32y10 \sqrt{2 y}+5 \sqrt{2 y}+3 \sqrt{2 y}102y​+52y​+32y​. 186y18 \sqrt{6 y}186y​ 182y18 \sqrt{2 y}182y​ 122y12 \sqrt{2 y}122y​ 186y318 \sqrt{6 y^{3}}186y3​

Studdy Solution

STEP 1

What is this asking? We're asked to combine like terms involving square roots.It's like adding apples together! Watch out! Don't multiply the numbers inside the square roots!We're adding, not multiplying.

STEP 2

1. Identify Like Terms2. Combine Coefficients3. Simplify the Expression

STEP 3

STEP 4

Since our terms are *like terms*, we can add their coefficients together.The **coefficients** are the numbers in front of the radical.So, we have 10+5+310 + 5 + 310+5+3.

STEP 5

Let's do the addition: 10+5+3=1810 + 5 + 3 = 1810+5+3=18. **Boom**!

STEP 6

Now, we just put it all together.We have 18\mathbf{18}18 as our combined coefficient, and the radical part stays the same, 2y\sqrt{2y}2y​.

STEP 7

So, our **simplified expression** is 182y18\sqrt{2y}182y​!We just added the coefficients and kept the radical part unchanged.It's like adding 10 apples + 5 apples + 3 apples = 18 apples!

STEP 8

The simplified expression is 182y18\sqrt{2y}182y​.

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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.

QuestionSimplify $10 \sqrt{2 y}+5 \sqrt{2 y}+3 \sqrt{2 y}$ . $18 \sqrt{6 y}$ $18 \sqrt{2 y}$ $12 \sqrt{2 y}$ $18 \sqrt{6 y^{3}}$

What is this asking? We're asked to combine like terms involving square roots.
It's like adding apples together! Watch out! Don't multiply the numbers inside the square roots!
We're adding, not multiplying.

1. Identify Like Terms
2. Combine Coefficients
3. Simplify the Expression

Since our terms are like terms, we can add their coefficients together.
The coefficients are the numbers in front of the radical.
So, we have $10 + 5 + 3$ .

Let's do the addition: $10 + 5 + 3 = 18$ . Boom!

Now, we just put it all together.
We have $\mathbf{18}$ as our combined coefficient, and the radical part stays the same, $\sqrt{2y}$ .

So, our simplified expression is $18\sqrt{2y}$ !
We just added the coefficients and kept the radical part unchanged.
It's like adding 10 apples + 5 apples + 3 apples = 18 apples!

The simplified expression is $18\sqrt{2y}$ .