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Solutions to Equations with Squares and Cubes

Authored by Anthony Clark

Mathematics

8th Grade

CCSS covered

Solutions to Equations with Squares and Cubes
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16 questions

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1.

FILL IN THE BLANK QUESTION

1 min • 1 pt

A perfect _________________ is the result after multiplying a number by itself three times.

Tags

CCSS.8.EE.A.2

2.

REORDER QUESTION

1 min • 6 pts

Media Image

What are the steps to solving this by completing the square?

Take the square root of both sides of the equation

Add 25 to both sides of the equation

Subtract 21 from both sides of the equation

Subtract 5 from both sides of the equation

Rewrite the left hand side as a (binomial)2

Answer explanation

Media Image

Steps for completing the square when a=1

1st: Rewrite as x2 + bx = c

2nd: Take half of b, square it, then add this to both sides.

3rd: Factor the perfect square trinomial.

4th: Take the square root of both sides and solve for both cases.

5th: Write the answer using curly braces in set notation

Tags

CCSS.HSA-REI.B.4B

3.

MULTIPLE CHOICE QUESTION

1 min • 5 pts

Media Image

Solve by the Square Root method: x2 = 16

± 4

± 8

4i

8i

-4i

Tags

CCSS.HSA-REI.B.4B

4.

DRAG AND DROP QUESTION

1 min • 6 pts

Media Image

If you have a ​ (a)   , you can solve the quadratic equation by square roots!

Remember a ​ (b)   number always has ​ (c)   real square roots, so you must solve for both cases.

difference of squares

perfect square trinomial

positive

negative

sum of cubes

difference of cubes

rational

two

one

three

Tags

CCSS.HSA-REI.B.4B

5.

MULTIPLE CHOICE QUESTION

1 min • 5 pts

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When is a quadratic equation factorable?

When the diagonal

(ax=y) is a perfect square

When the difference

(d=ax2−c) is a perfect square

When the difference

(d=ax2−c) is a perfect cube

When the discriminant

(d=b2−4ac) is a perfect cube

When the discriminant

(d=b2−4ac) is a perfect square

Tags

CCSS.HSA-REI.B.4B

6.

MULTIPLE SELECT QUESTION

1 min • 5 pts

Media Image

What is another word for roots of an equations?

(Select all choices that apply.)

y-intercepts

zeros

vertex

x-intercepts

solutions

Tags

CCSS.HSF-IF.C.7A

7.

REORDER QUESTION

1 min • 6 pts

Media Image

Order the following steps for solving quadratic equations by factoring.

Set each factor equal to zero, and solve each for the variable.

Write the answer using curly braces in set notation.

Factor the left side.

Set the quadratic equation equal to zero.

Tags

CCSS.HSA-REI.B.4B

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