Rational Exponents and Surds
31 - 5√5
(1 - 2√5)(1 - 3√5)
7√2-11
(1-√2)(4√2-3)
3√3
(12√3 x 2√5) ÷ 8√5
37+12√7
(2√7+3)²
8-5√2
(3-√8)(4+√2)
7+13√2
(3√2-1)(2√2+5)
13+5√5
(√5+1)(2√5+3)
1+√10
(√5-√2)(√5+2√2)
-√25
-5
√0.25
0.5
Anything raised to the zero power equals
1
√144
12
√(1÷16)
1÷4
√8
2√2
√12
2√3
√3 × √3
3
12√6
3√2 x 4√3
2+√3
4-√3-2(1-√3)
2√2
4√6 ÷ 2√3
8√2
5√2 + 3√2
√36
6
√8 × √8
8
What is a rational number
A number that can be written as a simple fraction
What is an irrational number
A number that cannot be written as a simple fraction
What is a surd
A surd is a number that has a 'nasty' square root such as √10 = 3.16227766 is a surd while the √16 = 4 is not a surd since the square root is a whole number.
16√15 + 80
Expand 8√5(2√3 + 2√5)
5+3√3
Express in the form a+b√3, (1+√3)(2+√3)
-43+√3
Express in the form a+b√3, (3√3+1)(2-5√3)
43-24√3
Express in the form a+b√3, (3√3-4)²
10+9√3
Express in the form a+b√3, (4+√3)(1+2√3)
Express in its simplest form √40
First find what 2 numbers multiplied together give us 40 (that is find the factors of 40) 1 x 40 2 x 20 4 x 10 5 x 8 Find a pair where one of the numbers is a square number, 4 x 10 will do since the square root of 4 is 2 So √40 = √(4 x 10) = √4 x √10 = 2 √10
If a product in parentheses is raised the a power, the parentheses indicate that ___ must be raised to that power.
each factor
A negative exponent indicates that we're dealing with a
fraction
If a whole number has a negative exponent, you have to turn it into a
fraction
To raise a power to a power, keep the same base and ___ the exponents.
multiply
An exponent of 1/2 is the same as a
square root
To divide two exponential expressions that have the same base, keep the base and ___ the exponents.
subtract
If an element on the bottom of a fraction has a negative exponent it means it belongs on the
top
2√3/3
Rationalise the denominator 2/√3
√6/12
Rationalise the denominator 3/2√54
5√21/6
Rationalise the denominator 3√175/2√27
√6
Rationalise the denominator 3√2/√3
4√10/9
Rationalise the denominator 4√20/3√18
√3/3
Rationalise the denominator √5/√15
2√5
Simplify √20
6√2
Simplify √72
3√2
Simplify √8 + √50 - √32
√7/21
Rationalise the denominator 1/3√7
√5/5
Rationalise the denominator 1/√5
√2/4
Rationalise the denominator 1/√8
√5/20
Rationalise the denominator 1/√80
√2
Rationalise the denominator 12/√72
2√7
Rationalise the denominator 14/√7
√-25
Undefined
What are we trying to do when simplifying a surd.
We are trying to get the smallest number possible inside the square root sign.
To multiply two exponential expressions that have the same base, keep the base and ___ the exponents
add
If an element on the top of a fraction has a negative exponent it means it belongs on the
bottom
In the expression 2x, the 2 is called the ___ of x.
coefficient
An exponent of 3/2 means first take the square root and then
cube it
2
√12 ÷ √3
√6
√3 x √2
3
√3 x √3
1
√3 ÷ √3
3+2√3
√3(2+√3)
6
√36
7
√49