This is an interactive set of flashcards testing your knowledge of perfect squares, square roots of perfect squares, powers of primes, and a few other important facts that successful GMAT students have at their fingertips. You will have 4 minutes to complete the set.

## Math Factor 1 - Squares, Square Roots, and Powers of Primes

Squares, Roots, and Powers of Primes is basically a math facts quiz. These basic facts should become your "friends," so that you can recognize them in context and use them to your advantage when performing seeminly difficult calculations.

Start

Congratulations - you have completed

*Math Factor 1 - Squares, Square Roots, and Powers of Primes*. You scored %%SCORE%% out of %%TOTAL%%. Your performance has been rated as %%RATING%%
Your answers are highlighted below.

Question 1 |

\(18^2\)

A | 284 |

B | 496 |

C | 324 |

D | 364 |

E | 360 |

Question 1 Explanation:

\(18^2 = 324\). The correct answer is D.

Question 2 |

\(25^2\)

A | 675 |

B | 625 |

C | 425 |

D | 725 |

E | 525 |

Question 2 Explanation:

\(25^2 = 625\). The correct answer is C.

Question 3 |

\(3^4\)

A | 27 |

B | 9 |

C | 12 |

D | 18 |

E | 81 |

Question 3 Explanation:

\(3^4 = 81\). The correct answer is A.

Question 4 |

\(2^6\)

A | 64 |

B | 24 |

C | 50 |

D | 32 |

E | 12 |

Question 4 Explanation:

\(2^6 = 64\). The correct answer is E.

Question 5 |

\(\sqrt{529}\)

A | 13 |

B | 23 |

Question 5 Explanation:

\(\sqrt{529} = 23\). The correct answer is B.

Question 6 |

\(2^5\)

A | 50 |

B | 32 |

C | 24 |

D | 64 |

E | 10 |

Question 6 Explanation:

\(2^5 = 32\). The correct answer is C.

Question 7 |

\(\sqrt{196}\)

A | 24 |

B | 16 |

C | 14 |

Question 8 |

\(\sqrt{2}\) is approximately

A | 1.6 |

B | 1.7 |

C | 1.3 |

D | 1.5 |

E | 1.4 |

Question 8 Explanation:

\(\sqrt{2}\) is approximately 1.4. The correct answer is B.

Question 9 |

\(14^2\)

A | 196 |

B | 156 |

C | 214 |

D | 96 |

E | 116 |

Question 9 Explanation:

\(14^2 = 196\). The correct answer is D.

Question 10 |

\({\sqrt{50}}^2\)

A | 100 |

B | 25 |

C | 50 |

Question 11 |

\(5^4\)

A | 1025 |

B | 500 |

C | 250 |

D | 125 |

E | 625 |

Question 11 Explanation:

\(5^4= 625\). The correct answer is B.

Question 12 |

\(3^3\)

A | 18 |

B | 36 |

C | 9 |

D | 27 |

E | 81 |

Question 12 Explanation:

\(3^3 = 27\). The correct answer is C.

Question 13 |

\(16^2\)

A | 116 |

B | 169 |

C | 256 |

D | 196 |

E | 216 |

Question 13 Explanation:

\(16^2 = 256\). The correct answer is A.

Question 14 |

\({\sqrt{x}}^2\)

A | \(|x|\) |

B | \(x\) |

C | \(-x\) |

Question 14 Explanation:

Square and square root are inverse operations, so you just end up where you started.

Question 15 |

\(\sqrt{576}\)

A | 26 |

B | 14 |

C | 24 |

D | 16 |

Question 15 Explanation:

\(\sqrt{576} = 24\). The correct answer is C.

Question 16 |

\(\sqrt{225}\)

A | 15 |

B | 25 |

Question 17 |

\(\sqrt{361}\)

A | 21 |

B | 19 |

Question 17 Explanation:

\(\sqrt{361} = 19\). The correct answer is B.

Question 18 |

\(23^2\)

A | 529 |

B | 429 |

C | 389 |

D | 469 |

E | 419 |

Question 18 Explanation:

\(23^2 = 529\). The correct answer is A.

Question 19 |

\({\sqrt{2}}^4\)

A | 8 |

B | 6 |

C | 1 |

D | 4 |

E | 2 |

Question 19 Explanation:

\({\sqrt{2}}^4 = {{\sqrt{2}}^2}^2 = 2^2 = 4\)

Question 20 |

\(\sqrt{289}\)

A | 13 |

B | 17 |

C | 23 |

Question 20 Explanation:

\(\sqrt{289} = 17\). The correct answer is B.

Question 21 |

\(7^2\)

A | 49 |

B | 7 |

C | 21 |

D | 35 |

E | 14 |

Question 21 Explanation:

\(7^2 = 49\). The correct answer is E.

Question 22 |

\(\sqrt{324}\)

A | 12 |

B | 22 |

C | 18 |

Question 22 Explanation:

\(\sqrt{324} = 18\). The correct answer is B.

Question 23 |

\(15^2\)

A | 125 |

B | 205 |

C | 30 |

D | 225 |

E | 250 |

Question 23 Explanation:

\(15^2 = 225\). The correct answer is D.

Question 24 |

\(2^{10}\)

A | 1024 |

B | 128 |

C | 64 |

D | 256 |

E | 512 |

Question 24 Explanation:

\(2^{10} = 1024\). The correct answer is A.

Question 25 |

\(21^2\)

A | 441 |

B | 461 |

C | 361 |

D | 121 |

E | 411 |

Question 25 Explanation:

\(21^2 = 441\). The correct answer is D.

Question 26 |

\(13^2\)

A | 296 |

B | 144 |

C | 169 |

D | 229 |

E | 289 |

Question 26 Explanation:

\(13^2 = 169\). The correct answer is B.

Question 27 |

\(19^2\)

A | 321 |

B | 211 |

C | 289 |

D | 249 |

E | 361 |

Question 27 Explanation:

\(19^2 = 361\). The correct answer is A.

Question 28 |

\(2^9\)

A | 32 |

B | 512 |

C | 64 |

D | 256 |

E | 128 |

Question 28 Explanation:

\(2^9 = 512\). The correct answer is E.

Question 29 |

\(17^2\)

A | 340 |

B | 229 |

C | 269 |

D | 189 |

E | 289 |

Question 29 Explanation:

\(17^2 = 289\). The correct answer is D.

Question 30 |

\(\sqrt{3}\) is approximately

A | 1.6 |

B | 1.3 |

C | 1.4 |

D | 1.7 |

E | 1.5 |

Question 30 Explanation:

\(\sqrt{3}\) is approximately 1.7. The correct answer is E.

Question 31 |

\(3^5\)

A | 81 |

B | 300 |

C | 243 |

D | 15 |

E | 27 |

Question 31 Explanation:

\(3^5 = 243\). The correct answer is D.

Question 32 |

\(\sqrt{625}\)

A | 15 |

B | 25 |

Question 32 Explanation:

\(\sqrt{625} = 25\). The correct answer is B.

Question 33 |

\(2^3\)

A | 2 |

B | 4 |

C | 8 |

D | 6 |

E | 9 |

Question 33 Explanation:

\(2^3 = 8\). The correct answer is D.

Question 34 |

\(7^3\)

A | 35 |

B | 49 |

C | 343 |

D | 140 |

E | 14 |

Question 34 Explanation:

\(7^3 = 343\). The correct answer is E.

Question 35 |

\(2^8\)

A | 32 |

B | 16 |

C | 128 |

D | 64 |

E | 256 |

Question 35 Explanation:

\(2^8 = 256.\) The correct answer is A.

Question 36 |

\(\sqrt{256}\)

A | 14 |

B | 16 |

C | 24 |

Question 36 Explanation:

\(\sqrt{256} = 16\). The correct answer is B.

Question 37 |

\(\sqrt{5}\) is approximately

A | 2.24 |

B | 2.14 |

C | 2.15 |

D | 2.25 |

E | 2.3 |

Question 37 Explanation:

\(\sqrt{5}\) is approximately 2.24. The correct answer is C.

Question 38 |

\(12^2\)

A | 184 |

B | 169 |

C | 144 |

D | 100 |

E | 132 |

Question 38 Explanation:

\(12^2 = 144\). The correct answer is C.

Question 39 |

\(5^2\)

A | 50 |

B | 10 |

C | 25 |

D | 15 |

E | 20 |

Question 39 Explanation:

\(5^2= 25\). The correct answer is D.

Question 40 |

\(24^2\)

A | 326 |

B | 376 |

C | 476 |

D | 576 |

E | 526 |

Question 40 Explanation:

\(24^2 = 576\). The correct answer is E.

Question 41 |

\(2^4\)

A | 14 |

B | 8 |

C | 10 |

D | 20 |

E | 16 |

Question 41 Explanation:

\(2^4\). The correct answer is 16.

Question 42 |

\(\sqrt{169}\)

A | 13 |

B | 23 |

Question 42 Explanation:

\(\sqrt{169} = 13\). The correct answer is A.

Question 43 |

If \(x \neq 0\), then \(x^0 = ?\)

A | 0 |

B | 1 |

Question 43 Explanation:

Anything to the zero power is 1!

Question 44 |

\(\sqrt{484}\)

A | 22 |

B | 18 |

C | 12 |

Question 44 Explanation:

\(\sqrt{484} = 22\). The correct answer is A.

Question 45 |

\(5^3\)

A | 625 |

B | 215 |

C | 125 |

D | 50 |

E | 25 |

Question 45 Explanation:

\(5^3 = 125\). The correct answer is C.

Question 46 |

\(\sqrt{x^2}\)

A | \(|x|\) |

B | \(x\) |

C | \(-x\) |

Question 46 Explanation:

\(\sqrt{anything^2} = |anything|\).

Question 47 |

\(3^2\)

A | 81 |

B | 9 |

C | 27 |

D | 6 |

E | 12 |

Question 47 Explanation:

\(3^2 = 9\). The correct answer is B.

Question 48 |

\(\sqrt{441}\)

A | 21 |

B | 19 |

C | 11 |

Question 48 Explanation:

\(\sqrt{441} = 21\) The correct answer is C

Question 49 |

\(22^2\)

A | 544 |

B | 404 |

C | 524 |

D | 444 |

E | 484 |

Question 49 Explanation:

\(22^2 = 484\). The correct answer is C.

Question 50 |

\(2^7\)

A | 128 |

B | 64 |

C | 14 |

D | 256 |

E | 32 |

Question 50 Explanation:

\(2^7 = 128\). The correct answer is B.

Once you are finished, click the button below. Any items you have not completed will be marked incorrect.
Get Results

There are 50 questions to complete.

← |
List |
→ |

Return

Shaded items are complete.

1 | 2 | 3 | 4 | 5 |

6 | 7 | 8 | 9 | 10 |

11 | 12 | 13 | 14 | 15 |

16 | 17 | 18 | 19 | 20 |

21 | 22 | 23 | 24 | 25 |

26 | 27 | 28 | 29 | 30 |

31 | 32 | 33 | 34 | 35 |

36 | 37 | 38 | 39 | 40 |

41 | 42 | 43 | 44 | 45 |

46 | 47 | 48 | 49 | 50 |

End |

Return

You have completed

questions

question

Your score is

Correct

Wrong

Partial-Credit

You have not finished your quiz. If you leave this page, your progress will be lost.

Correct Answer

You Selected

Not Attempted

Final Score on Quiz

Attempted Questions Correct

Attempted Questions Wrong

Questions Not Attempted

Total Questions on Quiz

Question Details

Results

Date

Score

Hint

Time allowed

minutes

seconds

Time used

Answer Choice(s) Selected

Question Text

All done

400 - Make some flashcards!

500 - Work those flashcards!

600
600 - Keep working those flashcards!

700 - Nice job, but you can do better!

800 - Who's the man!