Algebra: Substitution with Squares and Square Roots (3)

In this worksheet, students substitute numbers into expressions containing squares and square roots.

Key stage:  KS 3

Curriculum topic:   Algebra

Curriculum subtopic:   Substitute Numerical Values for Formulae/Expressions

Difficulty level:

QUESTION 1 of 10

When we substitute a number for a letter, we simply replace the letter with the number.

However, we must remember that 4b means 4 × b and 4b2 means 4 × b × b.

Example

Work out the value of the following expression when a = 4 and b = 9

3a2 - 7 - 2√ab

3a2 - 7 - 2√ab

= 3 × a × a - 7 - 2 × √a × b

= 3 × 4 × 4 - 7 - 2 × √4 × 9

= 48 - 7 - 2 × √36

= 48 - 7 - 2 × 6

= 48 - 7 - 12

= 29

Work out the value of the following expression when a = 2 and b = 1

3a2 - √4b

Work out the value of the following expression when a = 3 and b = 0

3a2 - √4b

Work out the value of the following expression when a = -3 and b = 0

3a2 - √4ab

Work out the value of the following expression when a = 9 and b = 1

4√a  + 5ab2

Work out the value of the following expression when a = 9 and b = 1

4√a  - 3ab2

Work out the value of the following expression when a = 4 and b = 2

3a2  + ab2

Work out the value of the following expression when a = 4 and b = 2

3√a  + ab2

Work out the value of the following expression when a = 4 and b = 2

3√a  - 2ab2

Work out the value of the following expression when a = 2 and b = 8

4a2 + √4ab

Work out the value of the following expression when a = 3 and b = 12

ba2 - √4ab

• Question 1

Work out the value of the following expression when a = 2 and b = 1

3a2 - √4b

10
EDDIE SAYS
12 - 2
• Question 2

Work out the value of the following expression when a = 3 and b = 0

3a2 - √4b

27
EDDIE SAYS
27 - 0
• Question 3

Work out the value of the following expression when a = -3 and b = 0

3a2 - √4ab

27
EDDIE SAYS
27 - 0
• Question 4

Work out the value of the following expression when a = 9 and b = 1

4√a  + 5ab2

57
EDDIE SAYS
12 + 45
• Question 5

Work out the value of the following expression when a = 9 and b = 1

4√a  - 3ab2

-15
EDDIE SAYS
12 - 27
• Question 6

Work out the value of the following expression when a = 4 and b = 2

3a2  + ab2

64
EDDIE SAYS
48 + 16
• Question 7

Work out the value of the following expression when a = 4 and b = 2

3√a  + ab2

22
EDDIE SAYS
6 + 16
• Question 8

Work out the value of the following expression when a = 4 and b = 2

3√a  - 2ab2

-26
EDDIE SAYS
6 - 32
• Question 9

Work out the value of the following expression when a = 2 and b = 8

4a2 + √4ab

24
EDDIE SAYS
16 + 8
• Question 10

Work out the value of the following expression when a = 3 and b = 12

ba2 - √4ab

96
EDDIE SAYS
108 - 12
---- OR ----

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