Rational vs Irrational
Is the number -1/7 rational or irrational?
Rational.
If a number can be written as a fraction of two integers (and the denominator isn't zero), it is a rational number.
The square root of 39 is between which two whole numbers?
6 and 7.
39 is between 36 and 49, so the square root of 39 is between the square roots of 36 and 49. In other words, square root of 39 is between 6 and 7.
The square root of 16 is...
4 because 4 x 4 = 16.
3 because 3 x 3 x 3 = 27.
Solve the equation for x.
x2 = 81
x = 9 OR x = -9
Is the number 0.23457439... rational or irrational?
Irrational.
Irrational numbers are nonterminating (do not end) and nonrepeating (do not follow a repeating pattern).
The square root of 61 is between what two whole numbers?
7 and 8.
61 is between 49 and 64, so the square root of 39 is between the square roots of 49 and 64. In other words, square root of 39 is between 7 and 8.
The square root of 0 is...
0 because 0 x 0 = 0.
The cube root of 1 is...
1 because 1 x 1 x 1 = 1.
Solve the equation for x.
x3 = 216
x = 6
Is the number π rational or irrational?
Irrational.
π ("pi") is a nonterminating, nonrepeating number.
The square root of 19 is between ___ and ___. It is closer to ___.
4 and 5; 4
19 is between 16 and 25, so the square root of 19 is between the square roots of 16 and 25. In other words, square root of 19 is between 4 and 5.
It is closer to 4 because 19 is closer to 16 than 25.
The square root of 81 is...
9 because 9 x 9 = 81.
The cube root of 64 is...
4 because 4 x 4 x 4 = 64.
Solve the equation for x.
x3 = 26
x = ∛26
Is the number 0.125125125... rational or irrational?
Rational.
Irrational numbers do not repeat, but this number does so it is rational.
The square root of 42 is between __ and __. It is closer to ___.
6 and 7; 6
42 is between 36 and 49, so the square root of 42 is between the square roots of 36 and 49. In other words, square root of 42 is between 6 and 7.
It is closer to 6 because 42 is closer to 36 than 49.
The square root of 196 is...
14 because 14 x 14 = 196.
The cube root of -8 is...
-2 because -2 x -2 x -2 = -8.
Solve the equation for x.
x2 = 99
x = ± √99
Is the number 0.393393339... rational or irrational?
Irrational.
The number is both nonterminating and nonrepeating (note that the digits after the decimal point do not do the same exact thing over and over, even though there are only 3s and 9s).
The square root of 21 is between __ and __. It is closer to __.
4 and 5; 5
21 is between 16 and 25, so the square root of 21 is between the square roots of 16 and 25. In other words, square root of 21 is between 4 and 5.
It is closer to 5 because 21 is closer to 25 than 16.
The square root of 225 is...
15 because 15 x 15 = 225.
The cube root of -125 is...
-5 because -5 x -5 x -5 = -125.
A cube has a volume of 64 cubic feet. How long is one side of the cube?
4 feet.