1.14 Simplifying surds
9 exam questions worth 21 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
0 / 21
What is \sqrt{12} in its simplest form?
Choose one answer.
Correct Not quite: the answer is \( 2\sqrt{3} \)
Mark scheme
B: 2\sqrt{3}
Model answer
2\sqrt{3} (B). 12 = 4 × 3, so √12 = √4 × √3 = 2√3.
Write \sqrt{50} in the form a\sqrt{2}.
Mark scheme
M1: √25 × √2; A1: 5√2
Model answer
50 = 25 × 2, so √50 = 5√2.
Write \sqrt{45} in the form a\sqrt{5}.
Mark scheme
M1: √9 × √5; A1: 3√5
Model answer
45 = 9 × 5, so √45 = 3√5.
Simplify \sqrt{6} \times \sqrt{3}. Give your answer in the form a\sqrt{b}.
Mark scheme
M1: √18; A1: 3√2
Model answer
√6 × √3 = √18 = √9 × √2 = 3√2.
Simplify \sqrt{8} + \sqrt{18}.
Mark scheme
M1: √8 = 2√2; M1: √18 = 3√2; A1: 5√2
Model answer
√8 = 2√2 and √18 = 3√2, so the sum is 5√2.
Expand and simplify (3 + \sqrt{2})(3 - \sqrt{2}).
Mark scheme
M1: 9 - 3√2 + 3√2 - 2; A1: 7
Model answer
9 - 3√2 + 3√2 - 2 = 7.
Expand and simplify (2 + \sqrt{3})^2.
Mark scheme
M1: (2 + √3)(2 + √3); M1: 4 + 2√3 + 2√3 + 3; A1: 7 + 4√3
Model answer
4 + 2√3 + 2√3 + 3 = 7 + 4√3.
Jo says that \sqrt{2} + \sqrt{3} = \sqrt{5}. Show that Jo is wrong.
Mark scheme
M1: calculates √2 + √3 (3.146...) or √5 (2.236...); A1: the values are different
Model answer
√2 + √3 = 1.414... + 1.732... = 3.146..., but √5 = 2.236..., so they are not equal. You cannot add unlike surds.
A right-angled triangle has shorter sides of 2 cm and 4 cm. (a) Work out the length of the hypotenuse. Give your answer in the form a\sqrt{b}. (b) Write down the exact perimeter of the triangle.
Mark scheme
M1: 2² + 4² = 20; M1: √20 = √4 × √5; A1: 2√5 cm; B1: 6 + 2√5 cm
Model answer
(a) h² = 4 + 16 = 20, so h = √20 = 2√5 cm. (b) Perimeter = 2 + 4 + 2√5 = 6 + 2√5 cm.
Found a mistake?