Rationalising the Denominator 2
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Question 1 of 6
1. Question
Rationalise the denominator:`1/(sqrt5)`Hint
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Great Work!
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For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt5``1/(sqrt5)` `=` `1/(sqrt5) xx ``(sqrt5)/(sqrt5)` `=` `(sqrt5)/(sqrt5 xx sqrt5)` `=` `(sqrt5)/(sqrt25)` Apply Multiplication Property `=` `(sqrt5)/5` `sqrt(25) = 5` `sqrt5 / 5` -
Question 2 of 6
2. Question
Rationalise the denominator:`3/(sqrt2)`Hint
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Correct!
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For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt2``3/(sqrt2)` `=` `3/(sqrt2) xx ``(sqrt2)/(sqrt2)` `=` `(3 xx sqrt2)/(sqrt2 xx sqrt2)` `=` `(3sqrt2)/(sqrt4)` Apply Multiplication Property `=` `(3sqrt2)/2` `sqrt(4) = 2` `(3sqrt2) / 2` -
Question 3 of 6
3. Question
Rationalise the denominator:`sqrt7/sqrt3`Hint
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Fantastic!
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For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt3``sqrt7/sqrt3` `=` `sqrt7/sqrt3 xx ``(sqrt3)/(sqrt3)` `=` `(sqrt7 xx sqrt3)/(sqrt3 xx sqrt3)` `=` `(sqrt21)/3` Apply Multiplication Property `(sqrt21)/3` -
Question 4 of 6
4. Question
Rationalise the denominator:`sqrt(10x)/sqrt6`Hint
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Excellent!
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For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt6``sqrt(10x)/sqrt6` `=` `sqrt(10x)/sqrt6 xx ``(sqrt6)/(sqrt6)` `=` `(sqrt(10x) xx sqrt6)/(sqrt6 xx sqrt6)` `=` `(sqrt(60x))/6` Apply Multiplication Property `=` `(sqrt(4xx15x))/6` Simplify the numerator `=` `(2sqrt(15x))/6` `=` `(sqrt(15x))/3` Reduce to lowest terms `(sqrt(15x))/3` -
Question 5 of 6
5. Question
Rationalise the denominator:`(sqrt3-1)/(6sqrt3)`Hint
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Nice Job!
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For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt3``(sqrt3-1)/(6sqrt3)` `=` `(sqrt3-1)/(6sqrt3) xx ``(sqrt3)/(sqrt3)` `=` `(sqrt3 xx (sqrt3-1))/(6sqrt3 xx sqrt3)` `=` `(3-sqrt3)/18` Apply Multiplication Property `(3-sqrt3)/18` -
Question 6 of 6
6. Question
Rationalise the denominator:`(sqrt5-sqrt3)/(sqrt5+sqrt3)`Hint
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Keep Going!
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Remember
For the answer to be in simplest form, the denominator should be a rational number.Multiply the numerator and the denominator by `sqrt5-sqrt3``(sqrt5-sqrt3)/(sqrt5+sqrt3)` `=` `(sqrt5-sqrt3)/(sqrt5+sqrt3) xx``(sqrt5-sqrt3)/(sqrt5-sqrt3)` `=` `((sqrt5-sqrt3)(sqrt5-sqrt3))/((sqrt5+sqrt3)(sqrt5-sqrt3))` `=` `(sqrt25-sqrt15-sqrt15+sqrt9)/(sqrt25-sqrt15+sqrt15-sqrt9)` Expand the brackets `=` `(5-2sqrt15+3)/(5-3)` `sqrt(25)=5` and `sqrt(9) = 3` `=` `(8-2sqrt15)/2` `=` `4-sqrt15` `4-sqrt15`
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- Simplify Surds with Variables 1
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- Simplify Surds with Variables 3
- Rewriting Entire and Mixed Surds 1
- Rewriting Entire and Mixed Surds 2
- Add and Subtract Surd Expressions (Basic) 1
- Add and Subtract Surd Expressions (Basic) 2
- Add and Subtract Surd Expressions (Basic) 3
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- Add and Subtract Surd Expressions 3
- Multiply Surd Expressions 1
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- Divide Surd Expressions 1
- Divide Surd Expressions 2
- Divide Surd Expressions 3
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