08. Surds – The Basics

Question 1

LEVEL 6

Simplify the following: \sqrt{96}

Select the correct answer from the list below:

A: 4\sqrt{6}

B: 8\sqrt{3}

C: 2\sqrt{3}

D: \sqrt{21}

CORRECT ANSWER: A: 4\sqrt{6}

WORKED SOLUTION:

Answer = 4\sqrt{6}

Question 2

LEVEL 6

Write \dfrac{\sqrt{20}}{\sqrt{5}}  in its simplest form.

Select the correct answer from the list below:

A: 4

B:\dfrac{\sqrt{20}}{\sqrt{5}}

C: \sqrt{\dfrac{20}{5}}

D: 2

CORRECT ANSWER: D: 2

WORKED SOLUTION:

Remember to use your rules for dividing surds.

\dfrac{\sqrt{20}}{\sqrt{5}}=\sqrt{\dfrac{20}{5}} = \sqrt{4} = 2

Question 3

LEVEL 6

Simplify \sqrt{3}+3\sqrt{3}

Select the correct answer from the list below:

A: \sqrt{3}

B: 3\sqrt{3}

C: 4\sqrt{3}

D: 2\sqrt{3}

CORRECT ANSWER: C: 4\sqrt{3}

WORKED SOLUTION:

Remember that there is an invisible 1 in front of the \sqrt{3}

Therefore in total there are 4 lots of  \sqrt{3}

Question 4

LEVEL 6

Expand and simplify (\sqrt{7} + \sqrt{5})(\sqrt{7} - \sqrt{5})

Select the correct answer from the list below:

A: 12

B: 12 + 2\sqrt{35}

C: 2

D: 24

CORRECT ANSWER: C: 2

WORKED SOLUTION:

(\sqrt{7} + \sqrt{5})(\sqrt{7} - \sqrt{5})

= {\sqrt{7}}^2 - \sqrt{5}\sqrt{7} + \sqrt{5}\sqrt{7} - {\sqrt{5}}^2

= 7 - \sqrt{35} + \sqrt{35} - 5 = 7 - 5

Question 5

LEVEL 6

Simplify 8\sqrt{10}+13\sqrt{10}-6\sqrt{10}-\sqrt{10}

Select the correct answer from the list below:

A: 15\sqrt{10}

B: 14\sqrt{40}

C: 14\sqrt{10}

D: 28\sqrt{10}

CORRECT ANSWER: D: 14\sqrt{10}

WORKED SOLUTION:

8\sqrt{10}+\sqrt{10}-6\sqrt{10}-\sqrt{10}

(8+13-6-1) \sqrt{10}=14×\sqrt{10}=14\sqrt{10}

Question 6

LEVEL 6

Expand and simplify 3(\sqrt{19}-4\sqrt{2})+3(\sqrt{5}+4\sqrt{2})

Select the correct answer from the list below:

A: 3\sqrt{5}+3\sqrt{2}

B: 3\sqrt{2}+2\sqrt{5}

C:  3\sqrt{5}+2\sqrt{19}

D: 3\sqrt{5}+3\sqrt{19}

CORRECT ANSWER: D: 3\sqrt{5}+3\sqrt{19}

WORKED SOLUTION:

3\sqrt{19}-12\sqrt{2}+3\sqrt{5}+12\sqrt{2}

(-12+12) \sqrt{2}+3\sqrt{5}+3\sqrt{19}

3\sqrt{5}+3\sqrt{19}

Question 7

LEVEL 6

Expand and simplify \sqrt{2}\times\sqrt{5}

Select the correct answer from the list below:

A:2\sqrt{5}

B: \sqrt{5+2}

C: \sqrt{10}

D: \sqrt{7}

CORRECT ANSWER: C: \sqrt{10}

WORKED SOLUTION:

\sqrt{2}\times \sqrt{5}=\sqrt{2\times 5}=\sqrt{10}