Real Numbers
What are Natural Numbers?
Natural Numbers are counting numbers: 1, 2, 3, .... and so on.
Simplify the expression
sqrt(8)/sqrt(2)
sqrt(4) = 2
Simplify
x^2+xy; use: x=2 and y=-2
(2)^2+(2)(-2)
4-4
0
Simplify
4x+7y-10-2x+y+11
4x-2x+7y+y-10+11
2x+8y+1
What are the first 12 perfect squares?
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
State if the following is rational or irrational and how you know.
5^2-sqrt6
5^2 =25 which is rational.
However, sqrt6 is irrational since 6 is not a perfect square.
The subtraction of a rational number and an irrational number is irrational.
Simplify the expression
sqrt2 * sqrt18
sqrt36 =6
Use the order of operations to simplify
4(6-2divide2)+2^2
4(6-1)+4
4(5)+4
20+4
24
Simplify
(x+5)(x-4)
x(x-4)+5(x-4)
x^2-4x+5x-20
x^2+x-20
How many terms are in the expression:
3x^4+8x^3-4x^2y-10xy^2-y+15
6 terms
State if the following is rational or irrational and how you know.
sqrt9 +4/5
sqrt9 = 3, which is rational.
Also, 4/5 is a fraction, which is rational.
The addition of rational numbers is rational.
Write the following in the simplest radical form
sqrt162
sqrt81 * sqrt2 =9sqrt2
Simplify
x^2+2(y-4)-x; use: x=3 and y=7
(3)^2+2(7-4)-3
9+2(3)-3
9+6-3
12
Simplify
6+2x^2-3x-7-2-4x+4x^2
2x^2+4x^2-3x-4x+6-7-2
6x^2-7x-3
Translate the phrase into an expression, where “a number” is the letter x.
The quotient of 8 and the sum of a number and 4
8/(x+4)
State all the subsets of The Real Number System pi belongs to.
Irrational Numbers
Real Numbers
Simplify the expression
sqrt(25x^4y^16)
sqrt25 sqrt(x^4) sqrt(y^16) =5x^2y^8
Simplify
(sqrt64 -(5-7)+10)/(6^2-7*4-3
(8-(-2)+10)/(36-28-3)
(8+2+10)/(8-3)
20/5 =4
Simplify
6(x^2-6x)+4(4x-7)
6x^2-36x+16x-28
6x^2-20x-28
Write the expression in words:
x^2+7
The sum of a number squared and 7.
State all the subsets of The Real Number System the number 7 belongs to.
Natural Numbers
Whole Numbers
Integers
Rational Numbers
Real Numbers
**Note the only subset it is NOT a part of is Irrational Numbers**
Simplify the expression
3sqrt(16x^10y^11)
3sqrt16 sqrt(x^10) sqrt(y^10) sqrty
3(4)(x^5)(y^5)sqrty
12x^5y^5sqrty
Simplify
(x+y^2-15)/(2z-xy) ; use: x=5, y=4, and z=13
(5+(4)^2-15)/(2(13)-(5)(4))
(5+16-15)/(26-20)
6/6 =1
Simplify
(2x-1)(3x-4)
2x(3x-4)-1(3x-4)
6x^2-8x-3x+4
6x^2-11x+4
State if the following is rational or irrational and how you know.
sqrt13 - sqrt13
sqrt13 is irrational.
However, when you subtract a number from itself the outcome is always 0.
sqrt13 - sqrt13 = 0 which is rational.