Surd – Questions

Note: a / b is supposed to be a fra: ction (Example: 1 / 2 is 1 over 2)

Writing Surds:

1a) Write (√5)² in the form of a, where a is an integer (1 mark)

1b) Write (2√5 + 3√6)² in the form of a+b√30, where a and b is a integer (2 marks)

1c) Write (√2√5 + 3√6) (2√5 – 3 √6) in the form of –a, where a is a integer (2 marks)

1d) Write √12 in the form a√3, where a is an integer (2 marks)

1e) Write √75 in the form a√3 where b is an integer (2 marks)

1f) Write √63 in the form a√7 where c is an integer (2 marks)

Simplifying Surds:

2a) Simplify √18 + √8, giving your answer in the form a√2, where a is an integer (2 marks)

2b) Simplify √24 +√96, giving your answer in the form b√6, where b is an integer (2 marks)

2c) Simplify √45 + √12, giving your answer in the form a√5 + b√3, where a and b are integers (3 marks)

Rationalising the denominator:

3a) Express 20 / √5 in the form a√5, where a is an integer (2 marks)

3b) Express 7 + √5 / √5 – 1, where a and b are integers (2 marks)

3c) Express 6 / 2+√3 in the form –a+b√3 / c, where a, b and c are integers (3 marks)

Other Surd Questions:

4a) Simplify √6 /2 multiplied by 8/√3 in the form a√2, where a is a integer (2 marks)

4b) Simplify √5(4+√5) in the form a+b√5, where a and b is a integer (2 marks)

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