What is the first step in solving the equation $$V=2\\sqrt[]{d}-5$$ for d?

Add 5 to both sides to isolate the radical: $$V + 5 = 2\\sqrt[]{d}$$ .

If $$V=75$$ , what is the length of the skid mark $$d$$ in the equation $$V=2\\sqrt[]{d}-5$$ ?

Substituting $$V=75$$ gives $$d=\frac{(75+5)^2}{4} = 1600$$ feet.

What is the formula to solve for d in the equation $$V=2\\sqrt[]{d}-5$$ ?

The formula is $$d=\frac{(V+5)^2}{4}$$ .

What happens if you square both sides of an equation incorrectly?

You may introduce extraneous solutions that do not satisfy the original equation.

What is the significance of the coefficient in the equation $$w=0.007d^3$$ ?

The coefficient indicates the proportionality constant that relates the variable $$d$$ to $$w$$ .

How can you determine the correct answer from multiple-choice options in radical equations?

Evaluate each option by substituting back into the original equation to see which one satisfies it.

What is the relationship between the length of a skid mark and the speed of a vehicle?

The length of the skid mark can be used to estimate the speed of the vehicle before brakes were applied.

What is the process of solving a radical equation?

1. Isolate the radical. 2. Square both sides. 3. Solve for the variable. 4. Check for extraneous solutions.

What does the term 'skid mark' refer to in the context of vehicle speed?

A skid mark is a mark left on the road by a vehicle that has skidded, which can be used to estimate the vehicle's speed.

Why is it important to check your solutions in radical equations?

To ensure that the solutions are valid and not extraneous, which can occur when squaring both sides of an equation.

Solving radical Equations Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Tags

CCSS.HSA.REI.A.2

2.

FLASHCARD QUESTION

Front

How do you isolate a variable in a radical equation?

Back

To isolate a variable, you can square both sides of the equation to eliminate the radical, then solve for the variable.

Tags

CCSS.HSA.REI.A.2

3.

FLASHCARD QUESTION

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Tags

CCSS.HSA.REI.A.2

4.

FLASHCARD QUESTION

Front

How do you check for extraneous solutions?

Back

Substitute the solution back into the original equation to see if it holds true.

Tags

CCSS.HSA.REI.A.2

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.A.2

6.

FLASHCARD QUESTION

Front

What do you do after isolating the radical in an equation?

Back

Square both sides of the equation to eliminate the radical.

Tags

CCSS.HSA.REI.A.2

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA.REI.A.2

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