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

\(25^2\)

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

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