Solving Quadratics with Square Roots Method and Imaginary Numbers

Authored by Anthony Clark

Mathematics

10th Grade

CCSS covered

Solving Quadratics with Square Roots Method and Imaginary Numbers

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19 questions

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DROPDOWN QUESTION

1 min • 4 pts

Equations such as x² + 1 = 0 have (a) , so mathematicians defined the (b) numbers to represent their solutions.
The imaginary unit, (c) , is defined as $\sqrt[]{-1}$ .
This is useful when working with square roots of negative numbers.

no real solution

1 real solution

2 real solutions

imaginary

fake

intangible

Tags

CCSS.HSN.CN.A.1

REORDER QUESTION

1 min • 4 pts

Reorder the following steps for solving quadratics by square roots.

If there is a NEGATIVE SQUARE ROOT, rewrite $\sqrt[]{-a}$ as $\sqrt[]{-1\cdot a}$ and break $a$ down if it is not a perfect square.

SIMPLIFY the radical, recalling that $\sqrt[]{-1}=i$

REWRITE the equation as x² = n

Take the SQUARE ROOT of both sides

SIMPLIFY the radical. Place "±" to indicate both answers.

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

1 min • 4 pts

Solve the equation using the square roots method:
x² − 64 = 0

x = ±8

x = ±64

x = ±32

x = ±16

x = ±4

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Solve by taking square roots:
2b² - 4 = -166

b = 9i, b = -9i

b = 3, b = -3

b = 9, b = -9

b = 3i, b = -3i

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Solve by taking the square root: -9k² = 225

4, -4

25i, -25i

-5i, 5i

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Tags

CCSS.8.EE.A.2

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Solve using square roots.

√3

±√3

-3

±i√3

Tags

CCSS.HSA-REI.B.4B

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Solve the quadratic with the square root method.

$\pm i\ \sqrt[]{39}$

$\sqrt[]{39}$

$\pm\ 39$

$\pm\sqrt[]{39}$

Tags

CCSS.HSA-REI.B.4B

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Solving Quadratics with Square Roots Method and Imaginary Numbers

Equations such as x2 + 1 = 0 have ​ (a) , so mathematicians defined the ​ (b) numbers to represent their solutions. The imaginary unit, ​ (c) , is defined as −1\sqrt[]{-1}−1​ .This is useful when working with square roots of negative numbers.

Reorder the following steps for solving quadratics by square roots.

Solve the equation using the square roots method: x2 − 64 = 0

Solve by taking square roots:2b2 - 4 = -166

Solve by taking the square root: -9k2 = 225

Solve using square roots.

Solve the quadratic with the square root method.

Solve the equation using the square roots method: 7x2 + 8 = 15

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Popular Resources on Wayground

Discover more resources for Mathematics

Equations such as x² + 1 = 0 have (a) , so mathematicians defined the (b) numbers to represent their solutions.
The imaginary unit, (c) , is defined as $\sqrt[]{-1}$ .
This is useful when working with square roots of negative numbers.

Solve the equation using the square roots method:
x² − 64 = 0

Solve by taking square roots:
2b² - 4 = -166

Solve by taking the square root: -9k² = 225

Solve the equation using the square roots method:
7x² + 8 = 15