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 |
\(2^{10}\)
A | 512 |
B | 1024 |
C | 128 |
D | 64 |
E | 256 |
Question 1 Explanation:
\(2^{10} = 1024\). The correct answer is A.
Question 2 |
If \(x \neq 0\), then \(x^0 = ?\)
A | 1 |
B | 0 |
Question 2 Explanation:
Anything to the zero power is 1!
Question 3 |
\(3^2\)
A | 27 |
B | 9 |
C | 6 |
D | 81 |
E | 12 |
Question 3 Explanation:
\(3^2 = 9\). The correct answer is B.
Question 4 |
\(17^2\)
A | 269 |
B | 340 |
C | 189 |
D | 289 |
E | 229 |
Question 4 Explanation:
\(17^2 = 289\). The correct answer is D.
Question 5 |
\(2^6\)
A | 12 |
B | 50 |
C | 64 |
D | 24 |
E | 32 |
Question 5 Explanation:
\(2^6 = 64\). The correct answer is E.
Question 6 |
\({\sqrt{2}}^4\)
A | 1 |
B | 6 |
C | 4 |
D | 8 |
E | 2 |
Question 6 Explanation:
\({\sqrt{2}}^4 = {{\sqrt{2}}^2}^2 = 2^2 = 4\)
Question 7 |
\(2^3\)
A | 2 |
B | 4 |
C | 9 |
D | 6 |
E | 8 |
Question 7 Explanation:
\(2^3 = 8\). The correct answer is D.
Question 8 |
\(7^3\)
A | 343 |
B | 14 |
C | 35 |
D | 49 |
E | 140 |
Question 8 Explanation:
\(7^3 = 343\). The correct answer is E.
Question 9 |
\(\sqrt{576}\)
A | 14 |
B | 26 |
C | 24 |
D | 16 |
Question 9 Explanation:
\(\sqrt{576} = 24\). The correct answer is C.
Question 10 |
\(5^4\)
A | 1025 |
B | 500 |
C | 625 |
D | 125 |
E | 250 |
Question 10 Explanation:
\(5^4= 625\). The correct answer is B.
Question 11 |
\(16^2\)
A | 216 |
B | 169 |
C | 116 |
D | 256 |
E | 196 |
Question 11 Explanation:
\(16^2 = 256\). The correct answer is A.
Question 12 |
\(22^2\)
A | 524 |
B | 544 |
C | 404 |
D | 484 |
E | 444 |
Question 12 Explanation:
\(22^2 = 484\). The correct answer is C.
Question 13 |
\(\sqrt{5}\) is approximately
A | 2.14 |
B | 2.24 |
C | 2.15 |
D | 2.25 |
E | 2.3 |
Question 13 Explanation:
\(\sqrt{5}\) is approximately 2.24. The correct answer is C.
Question 14 |
\(3^3\)
A | 9 |
B | 36 |
C | 27 |
D | 18 |
E | 81 |
Question 14 Explanation:
\(3^3 = 27\). The correct answer is C.
Question 15 |
\(19^2\)
A | 211 |
B | 321 |
C | 361 |
D | 249 |
E | 289 |
Question 15 Explanation:
\(19^2 = 361\). The correct answer is A.
Question 16 |
\(14^2\)
A | 156 |
B | 96 |
C | 116 |
D | 214 |
E | 196 |
Question 16 Explanation:
\(14^2 = 196\). The correct answer is D.
Question 17 |
\(\sqrt{196}\)
A | 16 |
B | 24 |
C | 14 |
Question 18 |
\({\sqrt{x}}^2\)
A | \(-x\) |
B | \(x\) |
C | \(|x|\) |
Question 18 Explanation:
Square and square root are inverse operations, so you just end up where you started.
Question 19 |
\(24^2\)
A | 326 |
B | 526 |
C | 376 |
D | 576 |
E | 476 |
Question 19 Explanation:
\(24^2 = 576\). The correct answer is E.
Question 20 |
\(\sqrt{256}\)
A | 16 |
B | 24 |
C | 14 |
Question 20 Explanation:
\(\sqrt{256} = 16\). The correct answer is B.
Question 21 |
\(3^5\)
A | 300 |
B | 27 |
C | 15 |
D | 243 |
E | 81 |
Question 21 Explanation:
\(3^5 = 243\). The correct answer is D.
Question 22 |
\(\sqrt{169}\)
A | 23 |
B | 13 |
Question 22 Explanation:
\(\sqrt{169} = 13\). The correct answer is A.
Question 23 |
\(\sqrt{x^2}\)
A | \(-x\) |
B | \(x\) |
C | \(|x|\) |
Question 23 Explanation:
\(\sqrt{anything^2} = |anything|\).
Question 24 |
\(\sqrt{324}\)
A | 22 |
B | 18 |
C | 12 |
Question 24 Explanation:
\(\sqrt{324} = 18\). The correct answer is B.
Question 25 |
\(21^2\)
A | 411 |
B | 121 |
C | 461 |
D | 441 |
E | 361 |
Question 25 Explanation:
\(21^2 = 441\). The correct answer is D.
Question 26 |
\(\sqrt{529}\)
A | 23 |
B | 13 |
Question 26 Explanation:
\(\sqrt{529} = 23\). The correct answer is B.
Question 27 |
\(\sqrt{484}\)
A | 18 |
B | 22 |
C | 12 |
Question 27 Explanation:
\(\sqrt{484} = 22\). The correct answer is A.
Question 28 |
\(2^4\)
A | 10 |
B | 14 |
C | 20 |
D | 16 |
E | 8 |
Question 28 Explanation:
\(2^4\). The correct answer is 16.
Question 29 |
\(2^7\)
A | 32 |
B | 128 |
C | 14 |
D | 256 |
E | 64 |
Question 29 Explanation:
\(2^7 = 128\). The correct answer is B.
Question 30 |
\(15^2\)
A | 30 |
B | 205 |
C | 225 |
D | 250 |
E | 125 |
Question 30 Explanation:
\(15^2 = 225\). The correct answer is D.
Question 31 |
\(\sqrt{3}\) is approximately
A | 1.6 |
B | 1.4 |
C | 1.3 |
D | 1.5 |
E | 1.7 |
Question 31 Explanation:
\(\sqrt{3}\) is approximately 1.7. The correct answer is E.
Question 32 |
\(7^2\)
A | 7 |
B | 35 |
C | 49 |
D | 21 |
E | 14 |
Question 32 Explanation:
\(7^2 = 49\). The correct answer is E.
Question 33 |
\(\sqrt{225}\)
A | 25 |
B | 15 |
Question 34 |
\(5^2\)
A | 20 |
B | 25 |
C | 10 |
D | 15 |
E | 50 |
Question 34 Explanation:
\(5^2= 25\). The correct answer is D.
Question 35 |
\(13^2\)
A | 144 |
B | 229 |
C | 289 |
D | 169 |
E | 296 |
Question 35 Explanation:
\(13^2 = 169\). The correct answer is B.
Question 36 |
\(2^5\)
A | 10 |
B | 64 |
C | 24 |
D | 50 |
E | 32 |
Question 36 Explanation:
\(2^5 = 32\). The correct answer is C.
Question 37 |
\(2^9\)
A | 256 |
B | 512 |
C | 64 |
D | 32 |
E | 128 |
Question 37 Explanation:
\(2^9 = 512\). The correct answer is E.
Question 38 |
\({\sqrt{50}}^2\)
A | 100 |
B | 50 |
C | 25 |
Question 39 |
\(23^2\)
A | 469 |
B | 429 |
C | 389 |
D | 529 |
E | 419 |
Question 39 Explanation:
\(23^2 = 529\). The correct answer is A.
Question 40 |
\(\sqrt{625}\)
A | 15 |
B | 25 |
Question 40 Explanation:
\(\sqrt{625} = 25\). The correct answer is B.
Question 41 |
\(\sqrt{2}\) is approximately
A | 1.6 |
B | 1.5 |
C | 1.4 |
D | 1.7 |
E | 1.3 |
Question 41 Explanation:
\(\sqrt{2}\) is approximately 1.4. The correct answer is B.
Question 42 |
\(3^4\)
A | 12 |
B | 18 |
C | 27 |
D | 81 |
E | 9 |
Question 42 Explanation:
\(3^4 = 81\). The correct answer is A.
Question 43 |
\(2^8\)
A | 64 |
B | 16 |
C | 256 |
D | 128 |
E | 32 |
Question 43 Explanation:
\(2^8 = 256.\) The correct answer is A.
Question 44 |
\(5^3\)
A | 25 |
B | 215 |
C | 125 |
D | 50 |
E | 625 |
Question 44 Explanation:
\(5^3 = 125\). The correct answer is C.
Question 45 |
\(\sqrt{441}\)
A | 21 |
B | 11 |
C | 19 |
Question 45 Explanation:
\(\sqrt{441} = 21\) The correct answer is C
Question 46 |
\(\sqrt{289}\)
A | 23 |
B | 17 |
C | 13 |
Question 46 Explanation:
\(\sqrt{289} = 17\). The correct answer is B.
Question 47 |
\(18^2\)
A | 364 |
B | 496 |
C | 284 |
D | 360 |
E | 324 |
Question 47 Explanation:
\(18^2 = 324\). The correct answer is D.
Question 48 |
\(25^2\)
A | 525 |
B | 425 |
C | 725 |
D | 625 |
E | 675 |
Question 48 Explanation:
\(25^2 = 625\). The correct answer is C.
Question 49 |
\(\sqrt{361}\)
A | 21 |
B | 19 |
Question 49 Explanation:
\(\sqrt{361} = 19\). The correct answer is B.
Question 50 |
\(12^2\)
A | 132 |
B | 184 |
C | 169 |
D | 144 |
E | 100 |
Question 50 Explanation:
\(12^2 = 144\). The correct answer is C.
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