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.

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Question 1 |

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

A | \(|x|\) |

B | \(x\) |

C | \(-x\) |

Question 1 Explanation:

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

Question 2 |

\(25^2\)

A | 725 |

B | 525 |

C | 425 |

D | 675 |

E | 625 |

Question 2 Explanation:

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

Question 3 |

\(3^5\)

A | 15 |

B | 300 |

C | 243 |

D | 27 |

E | 81 |

Question 3 Explanation:

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

Question 4 |

\(\sqrt{x^2}\)

A | \(x\) |

B | \(-x\) |

C | \(|x|\) |

Question 4 Explanation:

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

Question 5 |

\(5^2\)

A | 50 |

B | 25 |

C | 20 |

D | 10 |

E | 15 |

Question 5 Explanation:

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

Question 6 |

\(\sqrt{2}\) is approximately

A | 1.5 |

B | 1.4 |

C | 1.6 |

D | 1.7 |

E | 1.3 |

Question 6 Explanation:

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

Question 7 |

\(\sqrt{169}\)

A | 13 |

B | 23 |

Question 7 Explanation:

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

Question 8 |

\(\sqrt{289}\)

A | 13 |

B | 23 |

C | 17 |

Question 8 Explanation:

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

Question 9 |

\(17^2\)

A | 289 |

B | 189 |

C | 269 |

D | 340 |

E | 229 |

Question 9 Explanation:

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

Question 10 |

\(2^4\)

A | 14 |

B | 8 |

C | 10 |

D | 20 |

E | 16 |

Question 10 Explanation:

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

Question 11 |

\(18^2\)

A | 496 |

B | 284 |

C | 360 |

D | 364 |

E | 324 |

Question 11 Explanation:

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

Question 12 |

\(2^6\)

A | 12 |

B | 24 |

C | 32 |

D | 64 |

E | 50 |

Question 12 Explanation:

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

Question 13 |

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

A | 25 |

B | 50 |

C | 100 |

Question 14 |

\(3^3\)

A | 18 |

B | 27 |

C | 36 |

D | 81 |

E | 9 |

Question 14 Explanation:

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

Question 15 |

\(\sqrt{361}\)

A | 21 |

B | 19 |

Question 15 Explanation:

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

Question 16 |

\(2^{10}\)

A | 512 |

B | 256 |

C | 128 |

D | 1024 |

E | 64 |

Question 16 Explanation:

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

Question 17 |

\(7^3\)

A | 140 |

B | 343 |

C | 49 |

D | 14 |

E | 35 |

Question 17 Explanation:

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

Question 18 |

\(\sqrt{484}\)

A | 18 |

B | 22 |

C | 12 |

Question 18 Explanation:

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

Question 19 |

\(\sqrt{225}\)

A | 15 |

B | 25 |

Question 20 |

\(2^5\)

A | 24 |

B | 64 |

C | 32 |

D | 10 |

E | 50 |

Question 20 Explanation:

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

Question 21 |

\(\sqrt{256}\)

A | 24 |

B | 16 |

C | 14 |

Question 21 Explanation:

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

Question 22 |

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

A | 0 |

B | 1 |

Question 22 Explanation:

Anything to the zero power is 1!

Question 23 |

\(13^2\)

A | 169 |

B | 296 |

C | 289 |

D | 144 |

E | 229 |

Question 23 Explanation:

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

Question 24 |

\(19^2\)

A | 211 |

B | 289 |

C | 249 |

D | 321 |

E | 361 |

Question 24 Explanation:

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

Question 25 |

\(\sqrt{196}\)

A | 14 |

B | 16 |

C | 24 |

Question 26 |

\(\sqrt{441}\)

A | 11 |

B | 19 |

C | 21 |

Question 26 Explanation:

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

Question 27 |

\(\sqrt{625}\)

A | 25 |

B | 15 |

Question 27 Explanation:

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

Question 28 |

\(21^2\)

A | 411 |

B | 461 |

C | 361 |

D | 121 |

E | 441 |

Question 28 Explanation:

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

Question 29 |

\(2^3\)

A | 8 |

B | 9 |

C | 6 |

D | 2 |

E | 4 |

Question 29 Explanation:

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

Question 30 |

\(15^2\)

A | 205 |

B | 125 |

C | 250 |

D | 30 |

E | 225 |

Question 30 Explanation:

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

Question 31 |

\(\sqrt{5}\) is approximately

A | 2.25 |

B | 2.24 |

C | 2.3 |

D | 2.14 |

E | 2.15 |

Question 31 Explanation:

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

Question 32 |

\(3^4\)

A | 9 |

B | 27 |

C | 12 |

D | 81 |

E | 18 |

Question 32 Explanation:

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

Question 33 |

\(23^2\)

A | 529 |

B | 419 |

C | 389 |

D | 429 |

E | 469 |

Question 33 Explanation:

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

Question 34 |

\(7^2\)

A | 21 |

B | 49 |

C | 35 |

D | 7 |

E | 14 |

Question 34 Explanation:

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

Question 35 |

\(\sqrt{324}\)

A | 12 |

B | 22 |

C | 18 |

Question 35 Explanation:

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

Question 36 |

\(\sqrt{3}\) is approximately

A | 1.7 |

B | 1.4 |

C | 1.3 |

D | 1.5 |

E | 1.6 |

Question 36 Explanation:

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

Question 37 |

\(3^2\)

A | 9 |

B | 27 |

C | 81 |

D | 6 |

E | 12 |

Question 37 Explanation:

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

Question 38 |

\(2^9\)

A | 32 |

B | 128 |

C | 64 |

D | 512 |

E | 256 |

Question 38 Explanation:

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

Question 39 |

\(16^2\)

A | 169 |

B | 216 |

C | 196 |

D | 116 |

E | 256 |

Question 39 Explanation:

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

Question 40 |

\(5^4\)

A | 1025 |

B | 500 |

C | 125 |

D | 625 |

E | 250 |

Question 40 Explanation:

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

Question 41 |

\(\sqrt{576}\)

A | 26 |

B | 16 |

C | 24 |

D | 14 |

Question 41 Explanation:

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

Question 42 |

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

A | 6 |

B | 2 |

C | 1 |

D | 4 |

E | 8 |

Question 42 Explanation:

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

Question 43 |

\(2^7\)

A | 256 |

B | 64 |

C | 128 |

D | 14 |

E | 32 |

Question 43 Explanation:

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

Question 44 |

\(2^8\)

A | 16 |

B | 32 |

C | 256 |

D | 128 |

E | 64 |

Question 44 Explanation:

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

Question 45 |

\(5^3\)

A | 125 |

B | 25 |

C | 215 |

D | 50 |

E | 625 |

Question 45 Explanation:

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

Question 46 |

\(\sqrt{529}\)

A | 23 |

B | 13 |

Question 46 Explanation:

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

Question 47 |

\(24^2\)

A | 326 |

B | 526 |

C | 476 |

D | 576 |

E | 376 |

Question 47 Explanation:

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

Question 48 |

\(12^2\)

A | 184 |

B | 100 |

C | 132 |

D | 169 |

E | 144 |

Question 48 Explanation:

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

Question 49 |

\(22^2\)

A | 404 |

B | 484 |

C | 544 |

D | 524 |

E | 444 |

Question 49 Explanation:

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

Question 50 |

\(14^2\)

A | 96 |

B | 214 |

C | 156 |

D | 196 |

E | 116 |

Question 50 Explanation:

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

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