Rationalizing the Denominator 1
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Question 1 of 5
1. Question
Rationalise the denominator:`5/(4sqrt3)`Hint
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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``5/(4sqrt3)` `=` `5/(4sqrt3) xx ``(sqrt3)/(sqrt3)` `=` `(5 xx sqrt3)/(4sqrt3 xx sqrt3)` `=` `(5sqrt3)/(4sqrt9)` Apply Multiplication Property `=` `(5sqrt3)/(4 xx 3)` `sqrt(9) = 3` `=` `(5sqrt3)/12` `(5sqrt3)/12` -
Question 2 of 5
2. Question
Rationalise the denominator:`sqrt(5x^2)/sqrt8`Hint
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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 `sqrt8``sqrt(5x^2)/sqrt8` `=` `sqrt(5x^2)/sqrt8 xx ``(sqrt8)/(sqrt8)` `=` `(sqrt(5x^2) xx sqrt8)/(sqrt8 xx sqrt8)` `=` `(sqrt(40x^2))/8` Apply Multiplication Property `=` `(sqrt(4x^2xx10))/8` Simplify the numerator `=` `(2xsqrt10)/8` `=` `(xsqrt10)/4` Reduce to lowest terms `(xsqrt10)/4` -
Question 3 of 5
3. Question
Rationalise the denominator:`(8sqrt5)/(3sqrt2)`Hint
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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``(8sqrt5)/(3sqrt2)` `=` `(8sqrt5)/(3sqrt2) xx ``(sqrt2)/(sqrt2)` `=` `(8sqrt5 xx sqrt2)/(3sqrt2 xx sqrt2)` `=` `(8sqrt10)/(3sqrt4)` Apply Multiplication Property `=` `(8sqrt10)/(3 xx 2)` `sqrt(4) = 2` `=` `(8sqrt10)/6` `=` `(4sqrt10)/3` Simplify the fraction `(4sqrt10)/3` -
Question 4 of 5
4. Question
Rationalise the denominator:`(sqrt3+1)/(sqrt7)`Hint
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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 `sqrt7``(sqrt3+1)/(sqrt7)` `=` `(sqrt3+1)/(sqrt7) xx ``(sqrt7)/(sqrt7)` `=` `((sqrt3+1) xx sqrt7)/(sqrt7 xx sqrt7)` `=` `(sqrt7 xx sqrt3 + sqrt7 xx 1)/(sqrt7 xx sqrt7)` Apply Distributive Property `=` `(sqrt21+sqrt7)/(sqrt49)` Apply Multiplication Property `=` `(sqrt21+sqrt7)/(7)` `sqrt(49) = 7` `(sqrt21+sqrt7)/(7)` -
Question 5 of 5
5. Question
Rationalise the denominator:`1/(5+sqrt3)+1/(5-sqrt3)`Hint
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We can add two fractions by finding a common denominator. One common denominator is always the two denominators multiplied.For the answer to be in simplest form, the denominator should be a rational number.Find a common denominator by multiplying the denominators.`(5+sqrt3)(5-sqrt3)`Write the fraction sum using the common denominator`1/(5+sqrt3)+1/(5-sqrt3)` `=` `(1(5+sqrt3)+1(5-sqrt3))/((5+sqrt3)(5-sqrt3))` `=` `(5+sqrt3+5-sqrt3)/(25-5sqrt3+5sqrt3-sqrt3 xx sqrt3)` Expand the brackets `=` `(10)/(25-sqrt3 xx sqrt3)` `=` `(10)/(25-3)` `sqrt(3) xx sqrt(3) = 3` `=` `(10)/22` `10/22`
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