Common Core HSN.RN.B.3 worksheet

Question 1

Simplify: 2√6 + 8√6 − 2√6

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Question 2

Simplify √60 × √6. Give your answer in the form a√b (or a whole number).

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Question 3

Rationalise 1/(6 − √7). What is the denominator after rationalising?

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Question 4

Simplify: √252 − √28. Give your answer in the form a√b.

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Question 5

Rationalise and simplify: 9/(2 − √7)

• A. 18 + 9√7
• B. −6 + 3√7
• C. 6 − 3√7
• D. −6 − 3√7

Question 6

Expand and simplify: (7 + √2)(7 − √2)

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Question 7

Simplify 5√6 × 3√2. Give your answer in the form a√b.

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Question 8

Simplify √54 ÷ √3. Give your answer in the form a√b or as a whole number.

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Question 9

Simplify: 7√5 + 3√5 − 5√5

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Question 10

Simplify √30 × √3. Give your answer in the form a√b (or a whole number).

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Question 11

Rationalise 1/(5 + √3). What is the denominator after rationalising?

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Question 12

Simplify: √75 + √108. Give your answer in the form a√b.

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Question 13

Rationalise and simplify: 12/(3 + √5)

• A. 9 − 3√5
• B. 9 + 3√5
• C. 3 − 3√5
• D. −9 − 3√5

Question 14

Expand and simplify: (3 + √11)(3 − √11)

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Question 15

Simplify 4√6 × 3√3. Give your answer in the form a√b.

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Question 16

Simplify √54 ÷ √3. Give your answer in the form a√b or as a whole number.

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