Q.405. Solve using the square root prop... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.405. (page 982)

Solve using the square root property.
${(x - \frac{1}{4})}^{2} = \frac{3}{16}$

Short Answer

Expert verified

The solution is $x = - \frac{\sqrt{3}}{4} + \frac{1}{4}$ and $x = \frac{\sqrt{3}}{4} + \frac{1}{4}$ .

Step by step solution

Step 1. Given information.

The given equation is ${(x - \frac{1}{4})}^{2} = \frac{3}{16}$ .

Step 2. Apply the square root property.

The property states that if $x^{2} = k$ , then $x = 卤 \sqrt{k}$ .

Step 3. Simplify the equation.

${(x - \frac{1}{4})}^{2} = \frac{3}{16} x - \frac{1}{4} = 卤 \sqrt{\frac{3}{16}} x - \frac{1}{4} = 卤 \frac{\sqrt{3}}{4}$

Step 4. Solve the equation for x.

$\begin{array}{rcl} x - \frac{1}{4} & = & \frac{\sqrt{3}}{4} \\ x & = & \frac{\sqrt{3}}{4} + \frac{1}{4} \end{array}$ and $\begin{array}{rcl} x - \frac{1}{4} & = & - \frac{\sqrt{3}}{4} \\ x & = & - \frac{\sqrt{3}}{4} + \frac{1}{4} \end{array}$

Step 5. Simplified answer.

Hence, the required solution is $\begin{array}{rcl} x & = & \frac{\sqrt{3}}{4} + \frac{1}{4} \end{array}$ and $\begin{array}{rcl} x & = & - \frac{\sqrt{3}}{4} + \frac{1}{4} \end{array}$ .

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91影视

Solve using the square root property.
${(x - \frac{1}{4})}^{2} = \frac{3}{16}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the square root property.

Step 3. Simplify the equation.

Step 4. Solve the equation for x.

Step 5. Simplified answer.

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91影视

Solve using the square root property.x-142=316

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Apply the square root property.

Step 3. Simplify the equation.

Step 4. Solve the equation for x.

Step 5. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Mechanics Maths

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Calculus

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Solve using the square root property.
${(x - \frac{1}{4})}^{2} = \frac{3}{16}$