EXAMPLE 4 Solve: V3x + 6 = 0. Strategy Since 6 is outside the square root symbol, there are two terms on the left side of the equation. To isolate the radical, we will subtract 6 from both sides. Why This will put the equation in a form where we can square both sides to clear the radical. Solution 3x + 6 = 0 This is the equation to solve. V3x = -6 To isolate the radical on the left side, subtract 6 from both sides. (V3x)2 = (-6)2 Square both sides to eliminate the square root. 3x = To solve the resulting equation, divide both sides by 3. We check the proposed solution 12 in the original equation. V3x + 6 = V 3(12) + 6 Substitute 12 for x. = V 36 + 6 False. Since 12 does not satisfy the original equation, it is extraneous. The equation has no solution. The solution set is ø. Self Check Solve. (If there is no solution, enter NO SOLUTION.) Va - 2 + 2 = 0 a =
EXAMPLE 4 Solve: V3x + 6 = 0. Strategy Since 6 is outside the square root symbol, there are two terms on the left side of the equation. To isolate the radical, we will subtract 6 from both sides. Why This will put the equation in a form where we can square both sides to clear the radical. Solution 3x + 6 = 0 This is the equation to solve. V3x = -6 To isolate the radical on the left side, subtract 6 from both sides. (V3x)2 = (-6)2 Square both sides to eliminate the square root. 3x = To solve the resulting equation, divide both sides by 3. We check the proposed solution 12 in the original equation. V3x + 6 = V 3(12) + 6 Substitute 12 for x. = V 36 + 6 False. Since 12 does not satisfy the original equation, it is extraneous. The equation has no solution. The solution set is ø. Self Check Solve. (If there is no solution, enter NO SOLUTION.) Va - 2 + 2 = 0 a =
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Power Operation
Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus.
Exponents
The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.
Question
![## Example 4: Solving a Radical Equation
### Problem:
Solve the equation:
\[ \sqrt{3x} + 6 = 0 \]
### Strategy:
Since the constant 6 is outside the square root symbol, there are two terms on the left side of the equation. To isolate the radical, we will subtract 6 from both sides.
### Why:
This will put the equation in a form where we can square both sides to clear the radical.
### Solution:
\[ \sqrt{3x} + 6 = 0 \]
\[ \sqrt{3x} = -6 \]
To isolate the radical on the left side, subtract 6 from both sides.
\[ (\sqrt{3x})^2 = (-6)^2 \]
Square both sides to eliminate the square root.
\[ 3x = 36 \]
\[ x = 12 \]
To solve the resulting equation, divide both sides by 3.
We check the proposed solution \(12\) in the original equation:
\[ \sqrt{3x} + 6 = 0 \]
\[ \sqrt{3(12)} + 6 = ? \ 0 \]
Substitute \(12\) for \(x\).
\[ \sqrt{36} + 6 = ? \ 0 \]
\[ 6 + 6 = 0 \]
\[ 12 = 0 \]
False.
Since \(12\) does not satisfy the original equation, it is extraneous. The equation has no solution. The solution set is \(\varnothing\).
### Self Check:
Solve. (If there is no solution, enter NO SOLUTION.)
\[ \sqrt{a - 2} + 2 = 0 \]
\[ a = \] \[\_\_\_ \]
(Leave empty space for students to fill in the answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8585c01c-e95f-4e9e-ab09-9be83264bdef%2Fe0cccdef-6869-47b3-906e-a23f6be7ae85%2F7youppt_processed.png&w=3840&q=75)
Transcribed Image Text:## Example 4: Solving a Radical Equation
### Problem:
Solve the equation:
\[ \sqrt{3x} + 6 = 0 \]
### Strategy:
Since the constant 6 is outside the square root symbol, there are two terms on the left side of the equation. To isolate the radical, we will subtract 6 from both sides.
### Why:
This will put the equation in a form where we can square both sides to clear the radical.
### Solution:
\[ \sqrt{3x} + 6 = 0 \]
\[ \sqrt{3x} = -6 \]
To isolate the radical on the left side, subtract 6 from both sides.
\[ (\sqrt{3x})^2 = (-6)^2 \]
Square both sides to eliminate the square root.
\[ 3x = 36 \]
\[ x = 12 \]
To solve the resulting equation, divide both sides by 3.
We check the proposed solution \(12\) in the original equation:
\[ \sqrt{3x} + 6 = 0 \]
\[ \sqrt{3(12)} + 6 = ? \ 0 \]
Substitute \(12\) for \(x\).
\[ \sqrt{36} + 6 = ? \ 0 \]
\[ 6 + 6 = 0 \]
\[ 12 = 0 \]
False.
Since \(12\) does not satisfy the original equation, it is extraneous. The equation has no solution. The solution set is \(\varnothing\).
### Self Check:
Solve. (If there is no solution, enter NO SOLUTION.)
\[ \sqrt{a - 2} + 2 = 0 \]
\[ a = \] \[\_\_\_ \]
(Leave empty space for students to fill in the answer.)
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