Square Roots

Question 1

√0 = ?

Answer 1

0

Question 2

√1 = ?

Answer 2

1

Question 3

What are perfect squares?

Answer 3

When the numbers under the radicals (the square root sign) are whole numbers

Question 4

√(a/b) = ?

Answer 4

√b

Question 5

√(25/9) = ?

Answer 5

5/3

Question 6

√(7/36) = ?

Answer 6

6

Question 7

√(45/20) = ?

Answer 7

√(9/4) = 3/2

Question 8

√200 = ?

Answer 8

√(2)(2)(2)(5)(5) = (2)(5)√2 = 10√2

Question 9

4√7 + 5√11 + 6√7 - 9√11 = ?

Answer 9

(4√7 + 6√7) + (5√11 - 9√11) =

10√7 - 4√11

Question 10

(a√b)(c√d) = ?

Answer 10

ac√bd

Question 11

(3√3)(10√7) = ?

Answer 11

30√21

Question 12

(10√8)(3√10) = ?

Answer 12

(10) (3)√(2)(2)(2)(2)(5) =
(30) (2)(2)√5 =

120√5

Question 13

20
—- = ?
7√5

Answer 13

20 √5 20√5
—- x —- = ——-
7√5 √5 7(5)

20√5 4√5
—— = —–
35 7

Question 14

7
—– = ?
√45

Answer 14

7 7 √5 7√5 7√5
——— = —– X—– = —– = ——
√3)(3)(5) 3√5 √5 3(5) 15

Question 15

If c & d > 0, then which is greater?

√c + √d

√(c+d)

Answer 15

√c + √d

Question 16

If a >1, then which is greater?

a

√a

Answer 16

a

ex. 9 vs. √9

Question 17

If a=1, which is greater?

a

√a

Answer 17

They are the same

1

Question 18

If 0 < a < 1, which is greater?

a

√a

Answer 18

√a

Why? The square root of a positive number is closer to 1

Question 19

If a = 0, which is greater?

a

√a

Answer 19

They are the same.

0

Question 20

If a > 0 and √a < 1, which is greater?

1/√a

1

Answer 20

1/√a

Question 21

If √a > 1, then which is greater?

1/√a

1

Answer 21

1

Question 22

The square roof of a negative number is imaginary

Answer 22

This has not yet been seen on the GRE

Question 23

(√12 + √27)² = ?

Answer 23

[√(2)(2)(3) + √(3)(3)(3)]² =

(2√3 + 3√3)² =

(5√3)² =

25(3) =

75

Question 24

If 0 < a < 1, which is greater?

a²

√a

Answer 24

√a

Question 25

If you SQUARE a number between 0 and 1, it _______.

Answer 25

Moves closer to 0

Question 26

If you take the square root of a number between 0 and 1, it _____.

Answer 26

Moves closer to 1

Question 27

If 0 < a < 1, which is greater?

√a

√a³

Answer 27

√a

a > a³ and so are its square roots

Question 28

If 0 < a < 1, which is greater?

√a

1/√a⁷

Answer 28

1/√a⁷

If if a < 1, then a to any power will be < 1. (It will move closer to 0)

This means any fraction will be smaller.

Question 29

If c > 0, which is greater?

√c

1/√c

Answer 29

We don’t know. It all depends on if c is greater than, less than, or equal to 1

Question 30

Remember that with fractions, when the denominator is larger the _______

Answer 30

The amount is smaller