Surds

Question 1

√3 x √7

Answer 1

√3 x √7 = √21

Question 2

√24 ÷ √6

Answer 2

√24 ÷ √6 = √4 = 2

Question 3

2√3 x 3√5

Answer 3

2√3 x 3√5 = 6√15

Question 4

10√8 ÷ 2√2

Answer 4

10√8 ÷ 2√2 = 5√4 = 5x2= 10

Question 5

(√9)^2

Answer 5

(√9)^2 = √9 x √9 = √81= 9

Question 6

Express √75 in its simplest form

Answer 6

√75 simplified: √25 x √3 = 5√3

Question 7

Express √32 in its simplest form

Answer 7

√32 simplified: √16 x √2 = 4√2

Question 8

Write √18 in the form k√2, where k is an integer

Answer 8

√9 x √2 = 3√2

Question 9

Write 3√20 in the form k√5, where k is an integer

Answer 9

20 = √4 x √5 = 2√5 x 3= 6√5

Question 10

Simplify √40 + √90

Answer 10

√40 = √4 x √10 = 2√10
√90 = √9 x √10 = 3√10

2√10 + 3√10 = 5√10

You can add because there’s the same number inside the root.

Question 11

Simplify: √45 + √125 - √20

Answer 11

√9 x √5 + √25 x 5 - √4 x √5

3√5 + 5√5 - 2√5
= 6√5

Question 12

Simplify √3 + √12

Answer 12

√3 (can’t be simplified anymore)
√12 = √4 x √3 = 2√3

1√3 + 2√3 = 3√3

Question 13

Simplify √15 x √3

Answer 13

√45 = √9 x √5 = 3√5

Question 14

Simplify 3√6 x 2√3

Answer 14

6√18

√18 = √6 x √3
6 x √18 = 6√18

Question 15

Expand and simplify: √3(√3-2√5)

Answer 15

√9 - 2√15 = 3-2√15

Question 16

Simplify: 5√2 x 3√2

Answer 16

15√4 = 15 x 2 = 30

Question 17

√3 + √3

Answer 17

1√3 + 1√3 = 2√3

Question 18

(12 +8√5) ÷ 4

Answer 18

3 + 2√5

Question 19

(5 + 2√2)(3-√8)

Answer 19

15-5√8+6√2–2√16
-2√16 = -2 x 4 = 8

15 - 5√8+6√2–8

5√8 = √4 + √2 = (x5) 10√2

15 - 10√2 + 6√2 - 8

7 - 4√2

Question 20

Expand and simplify: (7 + 2√3)(2 - 3√6)

Answer 20

Fully simplified:
14 - 21√6 + 4√3 - 18√2

Question 21

Expand and simplify: (√12 - √3)^2

Answer 21

12 - 6 - 6 + 3= 3

Question 22

Find (5 - √8)(7 + √2) leaving your answer in the form a + b √2

Answer 22

35 + 5√2 - 7√8 - √16

Simplify √16 = 4, 7√8 = √4 x √2 = 7 x 2√2 = 14√2

(Don’t forget the minus in front of the 14√2)

31 + 5√2 - 14√2 =

31+ - 9√2 =

31 - 9√2