Math / Algebra

QuestionSolve $u^{2}=16$ , where $u$ is a real numbe Simplify your answer as much as pc
If there is more than one solution, If there is no solution, click on "No $u=$ $\square$

Studdy Solution

STEP 1

What is this asking? Find all real numbers $u$ such that $u$ multiplied by itself equals 16. Watch out! There might be more than one solution, so don't forget to consider both positive and negative possibilities!

STEP 2

1. Isolate $u$
2. Consider both positive and negative roots

STEP 3

To isolate $u$ , we need to undo the square.
The opposite of squaring a number is taking the square root.
So, let's take the square root of both sides of the equation $u^2 = 16$ .
Remember, whatever we do to one side of an equation, we must do to the other!
This gives us $\sqrt{u^2} = \sqrt{16}$ .

STEP 4

Now, $\sqrt{u^2}$ simplifies to $|u|$ (the absolute value of $u$ ), and $\sqrt{16}$ simplifies to 4.
So, our equation becomes $|u| = 4$ .
This is because the square root of a number squared is the absolute value of that number.

STEP 5

If $|u| = 4$ , then $u$ could be 4.
Let's check: $4 \cdot 4 = 16$ , which is true!

STEP 6

Remember, $|u| = 4$ also means $u$ could be -4.
Let's check this one too: $(-4) \cdot (-4) = 16$ , which is also true!
A negative times a negative is a positive!

STEP 7

So, we found two solutions for $u$ : $u = 4$ and $u = -4$ .

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QuestionSolve $u^{2}=16$ , where $u$ is a real numbe Simplify your answer as much as pc
If there is more than one solution, If there is no solution, click on "No $u=$ $\square$

Studdy Solution

STEP 1

What is this asking? Find all real numbers $u$ such that $u$ multiplied by itself equals 16. Watch out! There might be more than one solution, so don't forget to consider both positive and negative possibilities!

STEP 2

1. Isolate $u$
2. Consider both positive and negative roots

STEP 3

To isolate $u$ , we need to undo the square.
The opposite of squaring a number is taking the square root.
So, let's take the square root of both sides of the equation $u^2 = 16$ .
Remember, whatever we do to one side of an equation, we must do to the other!
This gives us $\sqrt{u^2} = \sqrt{16}$ .

STEP 4

Now, $\sqrt{u^2}$ simplifies to $|u|$ (the absolute value of $u$ ), and $\sqrt{16}$ simplifies to 4.
So, our equation becomes $|u| = 4$ .
This is because the square root of a number squared is the absolute value of that number.

STEP 5

If $|u| = 4$ , then $u$ could be 4.
Let's check: $4 \cdot 4 = 16$ , which is true!

STEP 6

Remember, $|u| = 4$ also means $u$ could be -4.
Let's check this one too: $(-4) \cdot (-4) = 16$ , which is also true!
A negative times a negative is a positive!

STEP 7

So, we found two solutions for $u$ : $u = 4$ and $u = -4$ .

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QuestionSolve u2=16u^{2}=16u2=16, where uuu is a real numbe Simplify your answer as much as pcIf there is more than one solution, If there is no solution, click on "No u=u=u= □\square□

Studdy Solution

STEP 1

What is this asking? Find all real numbers uuu such that uuu multiplied by itself equals 16. Watch out! There might be more than one solution, so don't forget to consider both positive and negative possibilities!

STEP 2

1. Isolate uuu2. Consider both positive and negative roots

STEP 3

STEP 4

Now, u2\sqrt{u^2}u2​ simplifies to ∣u∣|u|∣u∣ (the absolute value of uuu), and 16\sqrt{16}16​ simplifies to **4**.So, our equation becomes ∣u∣=4|u| = 4∣u∣=4.This is because the square root of a number squared is the absolute value of that number.

STEP 5

If ∣u∣=4|u| = 4∣u∣=4, then uuu could be **4**.Let's check: 4⋅4=164 \cdot 4 = 164⋅4=16, which is true!

STEP 6

Remember, ∣u∣=4|u| = 4∣u∣=4 also means uuu could be **-4**.Let's check this one too: (−4)⋅(−4)=16(-4) \cdot (-4) = 16(−4)⋅(−4)=16, which is also true!A negative times a negative is a positive!

STEP 7

So, we found *two* solutions for uuu: u=4u = 4u=4 and u=−4u = -4u=−4.

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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.

QuestionSolve $u^{2}=16$ , where $u$ is a real numbe Simplify your answer as much as pc
If there is more than one solution, If there is no solution, click on "No $u=$ $\square$

What is this asking? Find all real numbers $u$ such that $u$ multiplied by itself equals 16. Watch out! There might be more than one solution, so don't forget to consider both positive and negative possibilities!

1. Isolate $u$
2. Consider both positive and negative roots

Now, $\sqrt{u^2}$ simplifies to $|u|$ (the absolute value of $u$ ), and $\sqrt{16}$ simplifies to 4.
So, our equation becomes $|u| = 4$ .
This is because the square root of a number squared is the absolute value of that number.

If $|u| = 4$ , then $u$ could be 4.
Let's check: $4 \cdot 4 = 16$ , which is true!

Remember, $|u| = 4$ also means $u$ could be -4.
Let's check this one too: $(-4) \cdot (-4) = 16$ , which is also true!
A negative times a negative is a positive!

So, we found two solutions for $u$ : $u = 4$ and $u = -4$ .