Math Facts 1 – Squares, Roots, and Powers of Primes

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

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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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Your answers are highlighted below.

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

\(3^4\)

A	12
B	27
C	9
D	18
E	81

Question 2 Explanation:

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

Question 3

\(3^3\)

A	27
B	36
C	18
D	81
E	9

Question 3 Explanation:

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

Question 4

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

A	1
B	0

Question 4 Explanation:

Anything to the zero power is 1!

Question 5

\(3^2\)

A	27
B	81
C	9
D	12
E	6

Question 5 Explanation:

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

Question 6

\(3^5\)

A	300
B	27
C	243
D	81
E	15

Question 6 Explanation:

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

Question 7

\(\sqrt{x^2}\)

A	\(-x\)
B	\(x\)
C	\(\|x\|\)

Question 7 Explanation:

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

Question 8

\(2^{10}\)

A	64
B	256
C	128
D	1024
E	512

Question 8 Explanation:

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

Question 9

\(\sqrt{5}\) is approximately

A	2.25
B	2.24
C	2.3
D	2.15
E	2.14

Question 9 Explanation:

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

Question 10

\(\sqrt{484}\)

A	12
B	18
C	22

Question 10 Explanation:

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

Question 11

\(\sqrt{3}\) is approximately

A	1.5
B	1.6
C	1.3
D	1.7
E	1.4

Question 11 Explanation:

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

Question 12

\(5^4\)

A	250
B	500
C	125
D	1025
E	625

Question 12 Explanation:

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

Question 13

\(13^2\)

A	229
B	169
C	296
D	289
E	144

Question 13 Explanation:

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

Question 14

\(23^2\)

A	429
B	389
C	529
D	419
E	469

Question 14 Explanation:

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

Question 15

\(24^2\)

A	376
B	576
C	476
D	326
E	526

Question 15 Explanation:

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

Question 16

\(\sqrt{225}\)

A	25
B	15

Question 17

\(2^4\)

A	8
B	16
C	20
D	10
E	14

Question 17 Explanation:

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

Question 18

\(7^2\)

A	7
B	14
C	21
D	49
E	35

Question 18 Explanation:

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

Question 19

\(25^2\)

A	725
B	525
C	625
D	425
E	675

Question 19 Explanation:

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

Question 20

\(2^9\)

A	32
B	128
C	512
D	64
E	256

Question 20 Explanation:

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

Question 21

\(7^3\)

A	49
B	35
C	14
D	140
E	343

Question 21 Explanation:

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

Question 22

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

A	25
B	100
C	50

Question 23

\(5^3\)

A	125
B	625
C	25
D	50
E	215

Question 23 Explanation:

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

Question 24

\(2^3\)

A	6
B	4
C	8
D	9
E	2

Question 24 Explanation:

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

Question 25

\(\sqrt{2}\) is approximately

A	1.3
B	1.7
C	1.6
D	1.4
E	1.5

Question 25 Explanation:

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

Question 26

\(\sqrt{196}\)

A	14
B	16
C	24

Question 27

\(2^6\)

A	12
B	50
C	64
D	24
E	32

Question 27 Explanation:

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

Question 28

\(19^2\)

A	361
B	321
C	289
D	249
E	211

Question 28 Explanation:

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

Question 29

\(\sqrt{529}\)

A	13
B	23

Question 29 Explanation:

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

Question 30

\(2^5\)

A	64
B	10
C	24
D	50
E	32

Question 30 Explanation:

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

Question 31

\(2^7\)

A	14
B	128
C	64
D	256
E	32

Question 31 Explanation:

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

Question 32

\(12^2\)

A	184
B	100
C	132
D	144
E	169

Question 32 Explanation:

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

Question 33

\(2^8\)

A	64
B	16
C	128
D	256
E	32

Question 33 Explanation:

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

Question 34

\(18^2\)

A	364
B	496
C	360
D	324
E	284

Question 34 Explanation:

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

Question 35

\(14^2\)

A	214
B	196
C	116
D	156
E	96

Question 35 Explanation:

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

Question 36

\(\sqrt{361}\)

A	21
B	19

Question 36 Explanation:

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

Question 37

\(15^2\)

A	205
B	225
C	30
D	125
E	250

Question 37 Explanation:

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

Question 38

\(21^2\)

A	361
B	461
C	411
D	121
E	441

Question 38 Explanation:

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

Question 39

\(\sqrt{441}\)

A	19
B	21
C	11

Question 39 Explanation:

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

Question 40

\(\sqrt{256}\)

A	24
B	16
C	14

Question 40 Explanation:

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

Question 41

\(22^2\)

A	444
B	544
C	404
D	524
E	484

Question 41 Explanation:

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

Question 42

\(\sqrt{576}\)

A	14
B	16
C	24
D	26

Question 42 Explanation:

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

Question 43

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

A	2
B	8
C	4
D	1
E	6

Question 43 Explanation:

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

Question 44

\(\sqrt{169}\)

A	13
B	23

Question 44 Explanation:

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

Question 45

\(5^2\)

A	10
B	20
C	25
D	50
E	15

Question 45 Explanation:

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

Question 46

\(17^2\)

A	340
B	229
C	189
D	269
E	289

Question 46 Explanation:

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

Question 47

\(\sqrt{625}\)

A	15
B	25

Question 47 Explanation:

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

Question 48

\(\sqrt{289}\)

A	23
B	17
C	13

Question 48 Explanation:

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

Question 49

\(16^2\)

A	116
B	256
C	169
D	216
E	196

Question 49 Explanation:

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

Question 50

\(\sqrt{324}\)

A	12
B	18
C	22

Question 50 Explanation:

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

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

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