Question 1

Which of the following quadratic equations can be solved using the square root property without factoring or completing the square?

Accepted Answer

$x^2 - 9 = 0$

Question 2

What is the solution to $4x^2 - 25 = 0$ using the square root property?

Accepted Answer

$x = \pm \dfrac{5}{2}$

Question 3

If $x^2 + 16 = 0$, what type of roots will the equation have?

Accepted Answer

Imaginary (complex) roots

Question 4

Solve $2x^2 - 16 = 0$ using the square root property.

Accepted Answer

$x = \pm 2\sqrt{2}$

Question 5

Which step is NOT part of the square root property method for solving quadratic equations?

Accepted Answer

Factor the quadratic expression

Question 6

Given $x^2 = 5$, what are the solutions?

Accepted Answer

$x = \pm \sqrt{5}$

Question 7

A chemical reaction requires the temperature $T$ to satisfy $T^2 - 100 = 0$. What are the possible temperatures?

Accepted Answer

$T = \pm 10$

Question 8

If $x^2 + 25 = 0$, what is the solution?

Accepted Answer

$x = \pm 5i$

Question 9

Which equation is NOT factorable over the real numbers?

Accepted Answer

$x^2 + 4 = 0$

Question 10

A ball is thrown upward and its height $h$ (in meters) after $t$ seconds is given by $h = -4.9t^2 + 20$. At what time does the ball reach the ground? (Use the square root property.)

Accepted Answer

$t = \pm 2.02$

Question 11

Which of the following is a correct application of the square root property to solve $x^2 = -9$?

Accepted Answer

$x = \pm 3i$

Question 12

If $a$ and $c$ have the same sign in the standard form $ax^2 + bx + c = 0$ and $b = 0$, what type of solution will you get using the square root property?

Accepted Answer

Complex (imaginary) solutions

Question 13

Solve $\left(x - \dfrac{1}{2}\right)^2 = 5$ using the square root property.

Accepted Answer

$x = \dfrac{1}{2} \pm \sqrt{5}$

Question 14

Which method would be most appropriate to solve $x^2 - 5x = 0$?

Accepted Answer

Factoring

Question 15

A medical dosage formula requires solving $d^2 = 36$. What is the correct dosage $d$?

Accepted Answer

$d = \pm 6$

Question 16

If $x^2 = 0$, what is the solution?

Accepted Answer

$x = 0$

Question 17

Which of the following is a necessary first step when using the square root property?

Accepted Answer

Isolate the squared expression

Question 18

Solve $3x^2 = 27$ using the square root property.

Accepted Answer

$x = \pm 3$

Question 19

If $x^2 - 6x + 9 = 0$, which method is most efficient for solving?

Accepted Answer

Factoring

Question 20

A projectile's height is modeled by $h = 2t^2 - 8$. At what time $t$ does the projectile reach a height of $0$?

Accepted Answer

$t = \pm 2$

Solving Quadratic Equations: Square Root Property and Factoring

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