GMAT Problem Solving (PS) Forum - Free Practice Questions

ER

Complete 1000 GMAT Problem Solving Series (PS-1000 Series) Questions

Bunuel

03 Dec 2022, 14:23

321

12

151,221

by: ekfdskfe

13 Jul 2025, 19:03

ER

100 Hardest and easiest questions for PS as of March 2026

Bunuel

01 Jan 2026, 05:45

1.1k

8

312,267

by: Shashankksharma

17 Apr 2026, 02:55

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GMAT PS Question Directory by Topic & Difficulty

bb

16 Apr 2026, 14:28

3.3k

0

1,383,344

by: bb

16 Apr 2026, 14:28

ER

where k and m are positive integers. What is the greatest possible

655-705 (Hard) | Fractions and Ratios, Roots

655-705 (Hard) | Fractions and Ratios, Roots hide tags

Afroditee

11 Oct 2022, 12:29

24

5

4,647

by: Mehta17

07 Dec 2025, 18:47

ER

The value of cube root of (-89) is:

655-705 (Hard) | Roots

655-705 (Hard) | Roots hide tags

tejal777

03 Nov 2009, 18:23

209

14

35,570

by: bumpbot

02 Dec 2025, 13:49

ER

The value of (16pi/3)^(1/2) + 5^(1/2) is most nearly equal to which

Sub 505 (Easy) | Arithmetic, Roots

Sub 505 (Easy) | Arithmetic, Roots hide tags

HarveyKlaus

21 May 2017, 01:22

36

5

18,689

by: bumpbot

02 Dec 2025, 10:59

ER

√576800 is between

Sub 505 (Easy) | Roots

Sub 505 (Easy) | Roots hide tags

Bunuel

04 Jul 2018, 00:11

29

8

15,350

by: bumpbot

02 Dec 2025, 10:49

ER

Which of the following is not a factor of the solution to the equation

655-705 (Hard) | Algebra +2 tags

655-705 (Hard) | Algebra, Multiples and Factors, Roots hide tags

AndrewN

10 Feb 2021, 15:28

53

6

6,305

by: bumpbot

02 Dec 2025, 02:42

ER

If x and y are integers and (15^x + 15^(x+1))/4^y = 15^y wha

605-655 (Medium) | Exponents, Roots

605-655 (Medium) | Exponents, Roots hide tags

SnehaC

06 Oct 2017, 11:11

166

9

29,916

by: bumpbot

02 Dec 2025, 02:04

Given x<1, the expression ((x-1)^2)^(1/2) +1 is equivalent to which of

605-655 (Medium) | Absolute Values, Roots

605-655 (Medium) | Absolute Values, Roots hide tags

Russ19

08 Feb 2020, 10:09

62

5

7,224

by: bumpbot

01 Dec 2025, 20:34

ER

(root(9 + root(80)) + root(9 - root(80)))^2 =

605-655 (Medium) | Algebra, Roots

605-655 (Medium) | Algebra, Roots hide tags

smarinov

20 Jul 2022, 02:43

250

7

37,870

by: KarishmaB

01 Dec 2025, 09:14

ER

If x - 5 = x^(1/2) + 5^(1/2), what is the value of x ?

705-805 (Hard) | Algebra, Roots

705-805 (Hard) | Algebra, Roots hide tags

Bunuel

09 Dec 2022, 02:30

48

3

4,576

by: bumpbot

28 Nov 2025, 00:54

ER

What is the value of 6+... , where the given expression extends to an

555-605 (Medium) | Roots

555-605 (Medium) | Roots hide tags

Bunuel

01 Aug 2022, 12:15

8

2

2,095

by: bumpbot

25 Nov 2025, 18:13

ER

The cubic root of which of the following number is 3

655-705 (Hard) | Algebra, Roots

655-705 (Hard) | Algebra, Roots hide tags

Bunuel

16 Nov 2022, 09:31

24

2

4,195

by: bumpbot

25 Nov 2025, 15:02

ER

Find the value of expression

655-705 (Hard) | Algebra, Roots

655-705 (Hard) | Algebra, Roots hide tags

gmatcafe

09 Nov 2020, 21:47

41

3

4,977

by: bumpbot

25 Nov 2025, 14:42

ER

Which of the following is closest to the value of (√21 - √7)^2?

605-655 (Medium) | Algebra +2 tags

605-655 (Medium) | Algebra, Arithmetic, Roots hide tags

Bunuel

30 Jun 2018, 23:53

33

7

12,710

by: bumpbot

24 Nov 2025, 22:21

ER

If y > 0 , which of the following is equal to (45y^3)(1/2)?

Sub 505 (Easy) | Roots

Sub 505 (Easy) | Roots hide tags

guddo

29 Jan 2024, 07:55

7

2

3,562

by: bumpbot

24 Nov 2025, 15:51

ER

(2^(1/2) + 1)(2^(1/2) - 1)(3^(1/2) + 1)(3^(1/2) - 1) =

Sub 505 (Easy) | Algebra, Roots

Sub 505 (Easy) | Algebra, Roots hide tags

Bunuel

18 Sep 2018, 00:37

17

4

14,532

by: bumpbot

22 Nov 2025, 04:41

ER

Which of the following is always equal to sqrt(9+x^2-6x)?

555-605 (Medium) | Absolute Values, Roots

555-605 (Medium) | Absolute Values, Roots hide tags

GK_Gmat

14 May 2023, 12:39

203

10

32,928

by: luisdicampo

21 Nov 2025, 03:33

ER

\sqrt{7 + \sqrt{48}} - \sqrt{3} = ?

705-805 (Hard) | Algebra +2 tags

705-805 (Hard) | Algebra, Arithmetic, Roots hide tags

Bunuel

15 Mar 2014, 06:05

248

13

32,439

by: arushi118

20 Nov 2025, 09:52

ER

If y= (0.36x^8)^(1/2), then y =

Sub 505 (Easy) | Exponents, Roots

Sub 505 (Easy) | Exponents, Roots hide tags

Bunuel

16 May 2018, 04:39

2

3

2,600

by: bumpbot

12 Nov 2025, 05:41

ER

If x<0, which of the following must be true?

655-705 (Hard) | Inequalities +2 tags

655-705 (Hard) | Inequalities, Must or Could be True, Roots hide tags

Bunuel

27 Jun 2017, 00:38

75

17

14,635

by: bumpbot

11 Nov 2025, 10:05

ER

If @(n) is defined as the product of the cube root of n and

555-605 (Medium) | Algebra +3 tags

555-605 (Medium) | Algebra, Exponents, Functions and Custom Characters, Roots hide tags

GMATD11

21 Nov 2019, 02:28

128

15

17,774

by: bumpbot

09 Nov 2025, 09:54

ER

How many integer values of n satisfy the inequality 3√n > √n^3 ?

705-805 (Hard) | Inequalities, Roots

705-805 (Hard) | Inequalities, Roots hide tags

Bunuel

03 May 2021, 01:15

30

8

5,512

by: Bunuel

08 Nov 2025, 07:49

ER

What is the value of (9 - 65^(1/2))^(1/2) - (9 + 65^(1/2))^(1/2)^2 ?

655-705 (Hard) | Algebra, Roots

655-705 (Hard) | Algebra, Roots hide tags

taha1234

07 Jul 2021, 02:13

38

3

6,741

by: bumpbot

06 Nov 2025, 12:50

ER

Which of the following is equivalent to 21^(1/2)/6 ?

555-605 (Medium) | Roots

555-605 (Medium) | Roots hide tags

Bunuel

09 Feb 2017, 05:57

29

10

8,636

by: bumpbot

06 Nov 2025, 11:39

ER

What is the value of 10(root10(root10(...), where the given expression

655-705 (Hard) | Algebra, Roots

655-705 (Hard) | Algebra, Roots hide tags

Bunuel

17 Jun 2020, 05:48

32

3

5,270

by: bumpbot

06 Nov 2025, 07:21

ER

([[81(x^7)]^1/2]/[9x^4]^1/2) - [(162x^5)^1/2]/(27x^6) = ?

555-605 (Medium) | Exponents, Roots

555-605 (Medium) | Exponents, Roots hide tags

Bunuel

07 Oct 2021, 05:15

10

4

3,543

by: Bunuel

06 Nov 2025, 07:03

ER

Which of the following is the correct ordering of 2√13, 4√3, 5√2 and 3

605-655 (Medium) | Arithmetic +2 tags

605-655 (Medium) | Arithmetic, Inequalities, Roots hide tags

Bunuel

18 Oct 2018, 02:40

64

6

12,301

by: bumpbot

06 Nov 2025, 06:43

ER

NEW!!! Tough and tricky exponents and roots questions

655-705 (Hard) | Algebra +2 tags

655-705 (Hard) | Algebra, Exponents, Roots hide tags

1, 2, 3, 4

Bunuel

23 Sep 2024, 08:55

3.1k

74

572,342

by: Bunuel

06 Nov 2025, 00:35

ER

(180^(1/2) +45^(1/2))/135^(1/2)

555-605 (Medium) | Algebra, Roots

555-605 (Medium) | Algebra, Roots hide tags

Bunuel

25 Apr 2017, 03:08

37

7

8,898

by: bumpbot

04 Nov 2025, 17:57

ER

3\sqrt{80}+\frac{3}{9+4\sqrt{5}}}=

605-655 (Medium) | Roots

605-655 (Medium) | Roots hide tags

samark

20 Jul 2022, 02:51

98

10

20,265

by: bumpbot

03 Nov 2025, 07:18

ER

If 5*125^(1/x) = 1/(5^(1/x)), then x = ?

555-605 (Medium) | Exponents, Roots

555-605 (Medium) | Exponents, Roots hide tags

Bunuel

10 May 2017, 11:41

100

12

16,336

by: bumpbot

02 Nov 2025, 03:49

ER

Which of the following expressions can be written as an integer?

Sub 505 (Easy) | Algebra, Roots

Sub 505 (Easy) | Algebra, Roots hide tags

eybrj2

30 May 2025, 10:17

47

13

28,676

by: bumpbot

02 Nov 2025, 02:12

ER

(496)^(1/4) is between

505-555 (Easy) | Roots

505-555 (Easy) | Roots hide tags

jlgdr

17 Sep 2013, 17:28

112

7

24,046

by: Bunuel

01 Nov 2025, 08:00

ER

If r=0.345, s=(0.345)^2, and t=root(0.345), which of the

555-605 (Medium) | Exponents +2 tags

555-605 (Medium) | Exponents, Fractions and Ratios, Roots hide tags

Bunuel

06 May 2012, 09:47

223

9

31,773

by: bumpbot

31 Oct 2025, 08:55

ER

Find the value of x

555-605 (Medium) | Algebra, Roots

555-605 (Medium) | Algebra, Roots hide tags

ritula

04 Feb 2009, 02:04

104

17

18,912

by: bumpbot

27 Oct 2025, 02:34

ER

If (3-x)^(1/2) = (x)^(1/2) + 1, then 4x²=

655-705 (Hard) | Exponents, Roots

655-705 (Hard) | Exponents, Roots hide tags

MonkeyDDes

20 Aug 2021, 08:07

21

4

4,443

by: bumpbot

26 Oct 2025, 07:49

ER

A quadratic equation ax^2+bx+c=0 has two integral roots x1 and

805+ (Hard) | Algebra, Roots

805+ (Hard) | Algebra, Roots hide tags

mangamma

25 Apr 2019, 10:04

99

14

9,735

by: plpurva

22 Oct 2025, 22:19

ER

2^(1/2)/4 + 3/(2*2^(1/2)) =

505-555 (Easy) | Algebra, Roots

505-555 (Easy) | Algebra, Roots hide tags

guddo

24 Jan 2024, 08:42

32

4

7,301

by: Bunuel

22 Oct 2025, 06:02

ER

What is √82,944 ?

505-555 (Easy) | Roots

505-555 (Easy) | Roots hide tags

Bunuel

08 Jul 2017, 06:02

13

7

4,465

by: bumpbot

21 Oct 2025, 03:22

ER

The cube root of what integer power of 2 is closest to 50?

805+ (Hard) | Number Properties, Roots

805+ (Hard) | Number Properties, Roots hide tags

Bunuel

14 Sep 2015, 05:01

117

14

11,695

by: bumpbot

20 Oct 2025, 09:13

ER

Rounded to four decimal places, the square root of the square root of

805+ (Hard) | Fractions and Ratios, Roots

805+ (Hard) | Fractions and Ratios, Roots hide tags

Bunuel

27 Apr 2015, 04:31

130

12

15,465

by: Regor60

13 Oct 2025, 06:36

ER

Of the following, which is the closest approximation to 32/0.256^(1/2)

605-655 (Medium) | Arithmetic, Roots

605-655 (Medium) | Arithmetic, Roots hide tags

Bunuel

22 May 2020, 06:38

110

7

14,888

by: bumpbot

09 Oct 2025, 14:21

ER

The domain of the function f(x) = \sqrt{\sqrt{x+2} - \sqrt{4-x

655-705 (Hard) | Functions and Custom Characters, Roots

655-705 (Hard) | Functions and Custom Characters, Roots hide tags

Bunuel

13 Aug 2023, 06:00

416

17

52,754

by: egmat

08 Oct 2025, 06:08

ER

What is the value of (2*2^(1/2))(6^(1/2)) + 2*3^(1/2) ?

Sub 505 (Easy) | Exponents, Roots

Sub 505 (Easy) | Exponents, Roots hide tags

Bunuel

05 Jun 2023, 01:30

8

3

2,606

by: bumpbot

07 Oct 2025, 08:59

ER

(1 + 3^(1/2))(2 + 3^(1/2))^(1/2)

705-805 (Hard) | Algebra, Roots

705-805 (Hard) | Algebra, Roots hide tags

Bunuel

18 Mar 2023, 12:30

34

5

3,975

by: bumpbot

06 Oct 2025, 09:52

ER

If x = 1/(√11 + √10) and y =

605-655 (Medium) | Algebra, Roots

605-655 (Medium) | Algebra, Roots hide tags

BrentGMATPrepNow

01 Mar 2017, 09:08

42

4

6,250

by: Strategix

04 Oct 2025, 03:36

ER

Which of the following has the greatest value?

655-705 (Hard) | Fractions and Ratios +2 tags

655-705 (Hard) | Fractions and Ratios, Min-Max Problems, Roots hide tags

rahulms

25 Jan 2010, 00:20

108

13

17,592

by: bumpbot

02 Oct 2025, 08:26

ER

If x^(1/2) = 20 and y^(1/2) = 16, then (x^(1/2) + y^(1/2))/

605-655 (Medium) | Algebra, Roots

605-655 (Medium) | Algebra, Roots hide tags

Bunuel

03 Sep 2017, 06:03

33

4

5,933

by: bumpbot

02 Oct 2025, 02:51

ER

What is the value of 17^(1/2) + 47^(1/2), to the nearest whole number?

Sub 505 (Easy) | Arithmetic, Roots

Sub 505 (Easy) | Arithmetic, Roots hide tags

Bunuel

14 Oct 2019, 06:27

6

5

8,204

by: bot00078

02 Oct 2025, 02:28

ER

If x^(1/6) = 6, then √x^6 is ?

555-605 (Medium) | Exponents, Roots

555-605 (Medium) | Exponents, Roots hide tags

Carcass

31 Mar 2012, 01:22

45

14

28,920

by: bumpbot

25 Sep 2025, 02:37

ER

What is (1331)^(1/2)/(396^(1/2) + 275^(1/2))

555-605 (Medium) | Roots

555-605 (Medium) | Roots hide tags

Ekland

13 Feb 2016, 04:00

30

12

11,299

by: bumpbot

24 Sep 2025, 22:50