Algebra & Surds

BAT simplify and rationalise surdsBAT solve equations using the rules for indices and surds

√ AB=√ A √B √ CD

= √C√ D

√ X √ X=√X2=X

WB19Simplify a) √12 b) √ 49

16

c ¿√1200 d) √50+√18 e) √11×√11 f) √ 49

×√18

1

Algebra & Surds WB20 Simplify this expression √12+√3

WB21 Work out the Perimeter of each shape, give exact simplified answers

2

4 - 27

2 + 373 - 2

5 + 62

4 +2

12 - 2

4 - 22

45 - 1

5 - 2

11 + 25

Algebra & Surds WB22

Find length BC and express your answer as an exact simplified value

WB23B is (11 , 6) and C is ( 1.5, 10)

Show that length BC is 5√172

3

A C

B

Algebra & Surds WB24

Find the missing lengths and give the answers as simplified surds (all triangles are RATS)

4

Algebra & Surds WB25

5

Algebra & Surds WB26

work out the area of the rectanglegive an exact simplified answer

6

2−√3

4+√3

Algebra & Surds WB27ExamQ

A piece of rectangular card has a hole cut in it as shown a) Find the area of the large rectangle b) Find the area of the hole c) Express the area of the card that is left as a percentage of the area of the rectangle

[4]

WB28ExamQ

A corner piece of a design has cross section ABC in the shape of a right angled triangle as shown. k is a positive integer. Find the value of k

[5]

7

Algebra & Surds WB29 Explore making an integer

Multiply each of the given numbers by a single term to give an integer answer

√3

25

2 7

3 +2

Now set out the solutions to these carefully

(2 + 3)(2 - 3)

(1 + 5)(1 - 5)

(6 + 23)(6 - 23)

8

Algebra & Surds WB30

rationalise each surd

2√5

14+√7√7

1√3

42+√3

10√5

83−√3

√32√7

4+√23−√2

62√3

¿)

√3√2−√3

9

Algebra & Surds WB32

Simplify 4−√3√3

× 6+√34

WB33work out the value of A in this equation (6−A √2 )(6+ A√2)=33

WB3410

Algebra & Surds Solve the following equations, leaving each answers as a simplified surd

a) x √21=3

b) ( x−√3 )2=4

11