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