Question Solve $2y^2 - 96 = 0$ for real $y$ . Round your answer(s) to the nearest hundredth. If there is more than one solution, list them separated by commas. If there is no solution, click "No solution".

Studdy Solution

STEP 1

Assumptions
1. The given equation is $2y^{2} - 96 = 0$ .
2. We are solving for the real number $y$ .
3. If there are multiple solutions, they should be separated by commas.
4. The solutions should be rounded to the nearest hundredth.

STEP 2

To solve for $y$ , we first need to isolate the $y^2$ term. We can start by adding 96 to both sides of the equation.
$2y^{2} - 96 + 96 = 0 + 96$

STEP 3

Simplify the equation by combining like terms.
$2y^{2} = 96$

STEP 4

Next, we divide both sides of the equation by 2 to solve for $y^2$ .
$\frac{2y^{2}}{2} = \frac{96}{2}$

STEP 5

Simplify the equation to find $y^2$ .
$y^{2} = 48$

STEP 6

To find $y$ , we take the square root of both sides of the equation. Since we are looking for real number solutions, we consider both the positive and negative square roots.
$y = \pm\sqrt{48}$

STEP 7

Simplify the square root. We can rewrite $\sqrt{48}$ as $\sqrt{16 \times 3}$ to make it easier to simplify.
$y = \pm\sqrt{16 \times 3}$

STEP 8

Since $\sqrt{16} = 4$ , we can further simplify the square root.
$y = \pm4\sqrt{3}$

STEP 9

Now we approximate $\sqrt{3}$ to the nearest hundredth. $\sqrt{3}$ is approximately $1.73$ when rounded to the nearest hundredth.
$y \approx \pm4 \times 1.73$

STEP 10

Multiply 4 by 1.73 to find the approximate values of $y$ .
$y \approx \pm4 \times 1.73$

STEP 11

Calculate the positive and negative approximate values of $y$ .
$y \approx +4 \times 1.73 = +6.92$ $y \approx -4 \times 1.73 = -6.92$

STEP 12

List the solutions, separated by a comma, and rounded to the nearest hundredth.
$y \approx 6.92, -6.92$
The solutions to the equation $2y^{2} - 96 = 0$ are $y \approx 6.92$ and $y \approx -6.92$ , rounded to the nearest hundredth.

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Question Solve $2y^2 - 96 = 0$ for real $y$ . Round your answer(s) to the nearest hundredth. If there is more than one solution, list them separated by commas. If there is no solution, click "No solution".

Studdy Solution

STEP 1

Assumptions
1. The given equation is $2y^{2} - 96 = 0$ .
2. We are solving for the real number $y$ .
3. If there are multiple solutions, they should be separated by commas.
4. The solutions should be rounded to the nearest hundredth.

STEP 2

To solve for $y$ , we first need to isolate the $y^2$ term. We can start by adding 96 to both sides of the equation.
$2y^{2} - 96 + 96 = 0 + 96$

STEP 3

Simplify the equation by combining like terms.
$2y^{2} = 96$

STEP 4

Next, we divide both sides of the equation by 2 to solve for $y^2$ .
$\frac{2y^{2}}{2} = \frac{96}{2}$

STEP 5

Simplify the equation to find $y^2$ .
$y^{2} = 48$

STEP 6

To find $y$ , we take the square root of both sides of the equation. Since we are looking for real number solutions, we consider both the positive and negative square roots.
$y = \pm\sqrt{48}$

STEP 7

Simplify the square root. We can rewrite $\sqrt{48}$ as $\sqrt{16 \times 3}$ to make it easier to simplify.
$y = \pm\sqrt{16 \times 3}$

STEP 8

Since $\sqrt{16} = 4$ , we can further simplify the square root.
$y = \pm4\sqrt{3}$

STEP 9

Now we approximate $\sqrt{3}$ to the nearest hundredth. $\sqrt{3}$ is approximately $1.73$ when rounded to the nearest hundredth.
$y \approx \pm4 \times 1.73$

STEP 10

Multiply 4 by 1.73 to find the approximate values of $y$ .
$y \approx \pm4 \times 1.73$

STEP 11

Calculate the positive and negative approximate values of $y$ .
$y \approx +4 \times 1.73 = +6.92$ $y \approx -4 \times 1.73 = -6.92$

STEP 12

List the solutions, separated by a comma, and rounded to the nearest hundredth.
$y \approx 6.92, -6.92$
The solutions to the equation $2y^{2} - 96 = 0$ are $y \approx 6.92$ and $y \approx -6.92$ , rounded to the nearest hundredth.

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Question Solve 2y2−96=02y^2 - 96 = 02y2−96=0 for real yyy. Round your answer(s) to the nearest hundredth. If there is more than one solution, list them separated by commas. If there is no solution, click "No solution".

Studdy Solution

STEP 1

Assumptions1. The given equation is 2y2−96=02y^{2} - 96 = 02y2−96=0.2. We are solving for the real number yyy.3. If there are multiple solutions, they should be separated by commas.4. The solutions should be rounded to the nearest hundredth.

STEP 2

To solve for yyy, we first need to isolate the y2y^2y2 term. We can start by adding 96 to both sides of the equation.2y2−96+96=0+962y^{2} - 96 + 96 = 0 + 962y2−96+96=0+96

STEP 3

Simplify the equation by combining like terms.2y2=962y^{2} = 962y2=96

STEP 4

Next, we divide both sides of the equation by 2 to solve for y2y^2y2.2y22=962\frac{2y^{2}}{2} = \frac{96}{2}22y2​=296​

STEP 5

Simplify the equation to find y2y^2y2.y2=48y^{2} = 48y2=48

STEP 6

To find yyy, we take the square root of both sides of the equation. Since we are looking for real number solutions, we consider both the positive and negative square roots.y=±48y = \pm\sqrt{48}y=±48​

STEP 7

Simplify the square root. We can rewrite 48\sqrt{48}48​ as 16×3\sqrt{16 \times 3}16×3​ to make it easier to simplify.y=±16×3y = \pm\sqrt{16 \times 3}y=±16×3​

STEP 8

Since 16=4\sqrt{16} = 416​=4, we can further simplify the square root.y=±43y = \pm4\sqrt{3}y=±43​

STEP 9

Now we approximate 3\sqrt{3}3​ to the nearest hundredth. 3\sqrt{3}3​ is approximately 1.731.731.73 when rounded to the nearest hundredth.y≈±4×1.73y \approx \pm4 \times 1.73y≈±4×1.73

STEP 10

Multiply 4 by 1.73 to find the approximate values of yyy.y≈±4×1.73y \approx \pm4 \times 1.73y≈±4×1.73

STEP 11

Calculate the positive and negative approximate values of yyy.y≈+4×1.73=+6.92y \approx +4 \times 1.73 = +6.92y≈+4×1.73=+6.92 y≈−4×1.73=−6.92y \approx -4 \times 1.73 = -6.92y≈−4×1.73=−6.92

STEP 12

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Question Solve $2y^2 - 96 = 0$ for real $y$ . Round your answer(s) to the nearest hundredth. If there is more than one solution, list them separated by commas. If there is no solution, click "No solution".

Assumptions
1. The given equation is $2y^{2} - 96 = 0$ .
2. We are solving for the real number $y$ .
3. If there are multiple solutions, they should be separated by commas.
4. The solutions should be rounded to the nearest hundredth.

To solve for $y$ , we first need to isolate the $y^2$ term. We can start by adding 96 to both sides of the equation.
$2y^{2} - 96 + 96 = 0 + 96$

Simplify the equation by combining like terms.
$2y^{2} = 96$

Next, we divide both sides of the equation by 2 to solve for $y^2$ .
$\frac{2y^{2}}{2} = \frac{96}{2}$

Simplify the equation to find $y^2$ .
$y^{2} = 48$

To find $y$ , we take the square root of both sides of the equation. Since we are looking for real number solutions, we consider both the positive and negative square roots.
$y = \pm\sqrt{48}$

Simplify the square root. We can rewrite $\sqrt{48}$ as $\sqrt{16 \times 3}$ to make it easier to simplify.
$y = \pm\sqrt{16 \times 3}$

Since $\sqrt{16} = 4$ , we can further simplify the square root.
$y = \pm4\sqrt{3}$

Now we approximate $\sqrt{3}$ to the nearest hundredth. $\sqrt{3}$ is approximately $1.73$ when rounded to the nearest hundredth.
$y \approx \pm4 \times 1.73$

Multiply 4 by 1.73 to find the approximate values of $y$ .
$y \approx \pm4 \times 1.73$

Calculate the positive and negative approximate values of $y$ .
$y \approx +4 \times 1.73 = +6.92$ $y \approx -4 \times 1.73 = -6.92$