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Square Roots - The Basics Trivia Quiz

These questions are all about the basic properties of square roots. Only basic algebra is required for this quiz. Calculators won't be needed. Good Luck!

A multiple-choice quiz by rodney_indy. Estimated time: 5 mins.

Author
rodney_indy

Time
5 mins

Type
Multiple Choice

Quiz #
267,131

Updated
Jul 23 22

# Qns
10

Difficulty
Tough

Avg Score
6 / 10

Plays
699

One at a Time - Single Page - Timed Game

Question 1 of 10

1. How many square roots does a positive real number have? Hint

infinitely many

NEXT>

Question 2 of 10

2. Let A = (the square root of 8). Which of the following equals the square of A? Hint

4 * (the square root of 2)

2 * (the square root of 2)

8 * (the square root of 2)

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Question 3 of 10

3. The square root of 18 simplifies to what? Hint

6 * (the square root of 3)

9 * (the square root of 2)

3 * (the square root of 2)

2 * (the square root of 3)

NEXT>

Question 4 of 10

4. Let A = the square root of 6, B = the square root of 10, and C = the square root of 15. Which of the following is equal to the product ABC? Hint

10 * (the square root of 3)

15 * (the square root of 2)

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Question 5 of 10

5. (The square root of 12) divided by (the square root of 3) equals Hint

the square root of 2

the square root of 3

the square root of 6

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Question 6 of 10

6. The legs of a right triangle have lengths (the square root of 5) and (the square root of 12). What is the length of the hypotenuse? Hint

the square root of 13

the square root of 17

the square root of 60

the square root of 7

NEXT>

Question 7 of 10

7. Let A = 3 + (the square root of 7) and let B = 3 - (the square root of 7). Then the product AB equals Hint

NEXT>

Question 8 of 10

8. Which of the following is equal to the reciprocal of (4 + (the square root of 15))? Hint

(1/4) + (the square root of 15)/15

4 - (the square root of 15)

(1/4) - (the square root of 15)/15

(1/4) + (the square root of 15)/4

NEXT>

Question 9 of 10

9. Let a = 1 + (the square root of 3). Then a^2 = Hint

1 + 3 * (the square root of 3)

4 + (the square root of 3)

4 + 2 * (the square root of 3)

NEXT>

Question 10 of 10

10. You can show that (2 + (the square root of 5))^2 = 9 + 4 * (the square root of 5).

So my final question is this: What is the square root of (9 + 4 * (the square root of 5)) ? Hint

3 + (the square root of 5)

3 + 2 * (the square root of 5)

2 + (the square root of 5)

9 + 2 * (the square root of 5)

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Quiz Answer Key and Fun Facts

1. How many square roots does a positive real number have?

Answer: 2

Every nonzero real number has two square roots.

2. Let A = (the square root of 8). Which of the following equals the square of A?

Answer: 8

By the definition of square root, (the square root of 8) is a positive real number that when squared gives 8.

3. The square root of 18 simplifies to what?

Answer: 3 * (the square root of 2)

The square root of 18

= (the square root of 9) * (the square root of 2)

= 3 * (the square root of 2)

4. Let A = the square root of 6, B = the square root of 10, and C = the square root of 15. Which of the following is equal to the product ABC?

Answer: 30

Note that 6 = 2 * 3, 10 = 2 * 5, and 15 = 3 * 5. So 6 * 10 * 15 = 2^2 * 3^2 * 5^2, thus ABC = 2 * 3 * 5 = 30.

5. (The square root of 12) divided by (the square root of 3) equals

Answer: 2

(The square root of 12) divided by (the square root of 3) equals (the square root of (12/3)), which is (the square root of 4), which is 2.

6. The legs of a right triangle have lengths (the square root of 5) and (the square root of 12). What is the length of the hypotenuse?

Answer: the square root of 17

Let a = (the square root of 5), b = (the square root of 12), and c the length of the hypotenuse. By the Pythagorean Theorem, c^2 = a^2 + b^2. Now a^2 = 5 and b^2 = 12 by definition of square roots. So we have

c^2 = a^2 + b^2

= 5 + 12

=17 which means c = (the square root of 17).

7. Let A = 3 + (the square root of 7) and let B = 3 - (the square root of 7). Then the product AB equals

Answer: 2

Recall that (x + y)*(x - y) = x^2 - y^2.

So AB = 3^2 - (the square root of 7)^2

= 9 - 7

= 2.

B is called the conjugate of A (and vice-versa). If we wanted to rationalize the denominator of 1/A, we would multiply the fraction by (B/B).

8. Which of the following is equal to the reciprocal of (4 + (the square root of 15))?

Answer: 4 - (the square root of 15)

We want to rationalize the denominator of the fraction 1/(4 + (the square root of 15)), so multiply its numerator and denominator by the conjugate of the denominator, which is 4 - (the square root of 15). So you get

4 - (the square root of 15)
--------------------------------------------------------------
(4 + (the square root of 15) * (4 - (the square root of 15)

The product in the denominator equals 16 - (the square root of 15)^2, which equals 16 - 15, which is 1. So the answer is 4 - (the square root of 15).

9. Let a = 1 + (the square root of 3). Then a^2 =

Answer: 4 + 2 * (the square root of 3)

Recall that (A + B)^2 = A^2 + 2 * A * B + B^2.

Thus (1 + (the square root of 3))^2

= 1^2 + 2 * 1 * (the square root of 3) + (the square root of 3)^2

= 1 + 2 * (the square root of 3) + 3

= 4 + 2 * (the square root of 3)

[Don't forget the middle term!]

10. You can show that (2 + (the square root of 5))^2 = 9 + 4 * (the square root of 5). So my final question is this: What is the square root of (9 + 4 * (the square root of 5)) ?

Answer: 2 + (the square root of 5)

Since (2 + (the square root of 5))^2 = 9 + 4 * (the square root of 5), the square root of (9 + 4 * (the square root of 5)) is 2 + (the square root of 5). This is just the definition of square root. If the numbers were different, you would see this immediately: for example, 8^2 = 64, thus the square root of 64 is 8.

I hope you enjoyed this quiz! Thanks for playing!

Source: Author rodney_indy

This quiz was reviewed by FunTrivia editor crisw before going online.
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