Square Roots Flashcards
√0 = ?
0
√1 = ?
1
What are perfect squares?
When the numbers under the radicals (the square root sign) are whole numbers
√(a/b) = ?
√b
√(25/9) = ?
5/3
√(7/36) = ?
6
√(45/20) = ?
√(9/4) = 3/2
√200 = ?
√(2)(2)(2)(5)(5) = (2)(5)√2 = 10√2
4√7 + 5√11 + 6√7 - 9√11 = ?
(4√7 + 6√7) + (5√11 - 9√11) =
10√7 - 4√11
(a√b)(c√d) = ?
ac√bd
(3√3)(10√7) = ?
30√21
(10√8)(3√10) = ?
(10) (3)√(2)(2)(2)(2)(5) =
(30) (2)(2)√5 =
120√5
20
—- = ?
7√5
20 √5 20√5
—- x —- = ——-
7√5 √5 7(5)
20√5 4√5
—— = —–
35 7
7
—– = ?
√45
7 7 √5 7√5 7√5
——— = —– X—– = —– = ——
√3)(3)(5) 3√5 √5 3(5) 15
If c & d > 0, then which is greater?
√c + √d
√(c+d)
√c + √d
If a >1, then which is greater?
a
√a
a
ex. 9 vs. √9
If a=1, which is greater?
a
√a
They are the same
1
If 0 < a < 1, which is greater?
a
√a
√a
Why? The square root of a positive number is closer to 1
If a = 0, which is greater?
a
√a
They are the same.
0
If a > 0 and √a < 1, which is greater?
1/√a
1
1/√a
If √a > 1, then which is greater?
1/√a
1
1
The square roof of a negative number is imaginary
This has not yet been seen on the GRE
(√12 + √27)² = ?
[√(2)(2)(3) + √(3)(3)(3)]² =
(2√3 + 3√3)² =
(5√3)² =
25(3) =
75
If 0 < a < 1, which is greater?
a²
√a
√a
If you SQUARE a number between 0 and 1, it _______.
Moves closer to 0
If you take the square root of a number between 0 and 1, it _____.
Moves closer to 1
If 0 < a < 1, which is greater?
√a
√a³
√a
a > a³ and so are its square roots
If 0 < a < 1, which is greater?
√a
1/√a⁷
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.
If c > 0, which is greater?
√c
1/√c
We don’t know. It all depends on if c is greater than, less than, or equal to 1
Remember that with fractions, when the denominator is larger the _______
The amount is smaller
