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Rationalising the Denominator

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Powers and Roots Learning Material
Tutorial IDTitleTutorialVideo
Tutorial		Revision
Notes		Revision
Questions
7.5Rationalising the Denominator

Rationalising the Denominator Revision Questions

1. . What is the regular form of the fraction 3/√7?

  1. 3/7
  2. √3/√7
  3. 3√7/7
  4. √3/7

Correct Answer: C

2. . What is the simplest form of the fraction 10√3/√5 ?

  1. 5
  2. 2√15
  3. 10√15/5
  4. 10√15

Correct Answer: B

3. . What is the regular form of the expression √2/1 - √3?

  1. -√2(1 + √3)/2
  2. √2(1 + √3)/2
  3. √2(1 - √3)/2
  4. 1 - √3/√2

Correct Answer: A

4. . Which is the equivalent expression of

√8/√2 - 1

after rationalising the denominator?

  1. 4 + 2√2
  2. 4 + √2
  3. 2 + √2
  4. 4 + √2/2

Correct Answer: A

5. . What is the simplest form of the expression

1/1 + 1/√5
  1. 5 - √5/4
  2. 5 - √5/5
  3. 5 + √5/4
  4. 5 + √5/5

Correct Answer: A

6. . Write the expression

2/2 - √2

in the form a + b√c, where a, b and c are integers.

  1. 4 + 2√2
  2. 2 + 2√2
  3. 2 + √2
  4. 1 + √2

Correct Answer: C

7. . What is the value of a, b and c if the expression

3/2 + √3
is written in the form a+b√c.
  1. a = 6; b = -3; c = 3
  2. a = -6; b = 3, c = -3
  3. a = -6; b = -3; c = 3
  4. a = -6; b = 3; c = 3

Correct Answer: D

8. . A rectangle has a width of (4 - √10) cm and an area of 240 cm2. Find the length of the rectangle by expressing the answer in the form a + b√10 where a and b are integers. Recall the formula Area = Length × Width used to calculate the area of a rectangle.

  1. 16 + 4√10
  2. 16 + 40√10
  3. 160 + 40√10
  4. 140 + 40√10

Correct Answer: C

9. . The dimensions of a rectangle are (5 - √2) cm and y cm where y is the width. What is the width of this rectangle if the area is 23 cm2? Recall the formula Area = Length × Width used to calculate the area of a rectangle.

  1. 5 + √2
  2. 5 + 2√2
  3. 5 - 2√2
  4. 10 + √2

Correct Answer: A

10. . What is the regular form of the algebraic fraction

2/3√x
  1. 2/3x
  2. 2√x
  3. 2√x/3
  4. 2√x/3x

Correct Answer: D

11. . What is the regular form of the fraction √18/24 ?

  1. √3/4
  2. √3/4
  3. √3/2
  4. 3/√4

Correct Answer: C

12. . What is the regular form of the fraction √80/36 ?

  1. 4√5/6
  2. 2√5/3
  3. √5/3
  4. √5/6

Correct Answer: B

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