Rational or Irrational?
Is the number 2.121121112... rational or irrational?
Irrational (It is a non-terminating, non-repeating decimal).
The value of
sqrt 85
is between which two consecutive integers?
9 and 10 (Because
sqrt 81 =9
sqrt 100 = 10
Simplify:
a^4*a^3
a^7
Simplify:
x^9/x^4
x^5
(Subtract exponents)
Which is greater: 32 or 23?
32 (9 is greater than 8).
Which of these is rational:
pi/4
or
sqrt 144/ sqrt 100
sqrt 144/ sqrt 100 12/10 or 1.2
because it simplifies to
If you are plotting
-sqrt 17
on a number line, between which two integers would you place a dot?
Between -4 and-5 (Because
sqrt 16 =4
, so
-sqrt 17
is just past -4).
Simplify the coefficients (numbers) only:
4x^2*3x^5
12 (Because 4 x 3 = 12)
Simplify:10x5 / 2x2
5x3 (Divide numbers, subtract exponents)
Arrange from least to greatest:
5.1, 4.9, sqrt 25
4.9, sqrt 25=5, 5.1
True or False: The set {3, 2, 1, -0.75,
pi
} consists only of rational numbers.
False (Because
pi
is irrational)
Is
sqrt 50
closer to 7 or 8?
7. (It is very close to
sqrt 49
Simplify the variables only:
4x^2*3x^5
x^7
(Because 2 + 5 = 7).
Rewrite
5^-2
without a negative exponent
1/5^2 OR 1/25
Which list is in order from least to greatest?
A)
sqrt{10}, 3.5, \pi
B)
\pi, \sqrt{10}, 3.5
B (\pi \approx 3.14, \sqrt{10} \approx 3.16, 3.5)
Why can the value of
pi
not be written as a ratio of two integers?
Because it is an irrational number (or: its decimal expansion never terminates or repeats)
Which point on a number line best represents
sqrt 8
?
A) Exactly on 3
B) A little less than 3
C) A little more than 2
B (A little less than 3, since
sqrt 9 = 3
Simplify completely:
(3y^2)^3
27y^6
(Cube the 3 to get 27, multiply 2 x 3 for the exponent).
Simplify to a single positive exponent: 4y2 /4y6
1/y^4
Place the following in order from least to greatest:
4, \sqrt{15}, and 3.5
3.5, \sqrt{15}, 4
Explanation: 3.5 is the smallest.
\sqrt{15}
is just under 4 (approx 3.87). 4 is the largest.
Identify the irrational number in this list:
sqrt 100, sqrt 18, 0.333..., -5
sqrt 18
(It is not a perfect square)
How much greater is
sqrt 26
than
sqrt 17
?
A) Exactly 9
B) Less than 1
C) A little more than 1
B (Less than 1.
sqrt 26
~~
5.1 and
sqrt 17
~~
4.1. The gap between roots shrinks as numbers get higher)
Find the error: A student simplified
(2x^5)^2
and got
4x^7
. What did they do wrong?
They added the exponents (5+2) instead of multiplying them (5 x 2). The correct answer is
4x^10
Simplify completely: -20a6b3/5a2b
-4a4b2 (Divide -20 by 5, subtract a exponents, subtract b exponents)
Arrange from least to greatest:
2\sqrt{9}, \sqrt{40}, 6.1.
Answer:
2\sqrt{9}, 6.1, \sqrt{40}.
Why?
2\sqrt{9} = 2(3) = 6
6.1 = 6.1
\sqrt{40} \approx 6.3 sqrt 36 = 6)
.