4 ESO Academics - Unit 02 - Exercises 4.2.3 - Rationalizing the Denominator and Standard Form

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UNIT 02 October
1. Rationalize the denominator:
2. Rationalize the denominator:
3. Solve:
4. Rationalize the denominator:
5. Rationalize the denominator
𝟏𝟏 + √𝟑𝟑
𝟏𝟏 − √𝟐𝟐
=
𝟓𝟓
𝟑𝟑 − √𝟓𝟓
=
√𝟓𝟓
𝟑𝟑 − √ 𝟕𝟕
=
𝟒𝟒
√ 𝟕𝟕
=
−𝟔𝟔
√𝟐𝟐
𝟑𝟑 =
−𝟑𝟑
√𝟐𝟐
=
𝟏𝟏𝟏𝟏
√𝟓𝟓𝟑𝟑𝟖𝟖 =
−𝟐𝟐
𝟐𝟐 + √𝟔𝟔
=
𝟏𝟏
√𝟑𝟑 + √𝟓𝟓
=
𝟐𝟐
𝟑𝟑 + √𝟑𝟑
𝟒𝟒 =
√𝟓𝟓
√𝟑𝟑
=
𝟓𝟓
−𝟐𝟐√ 𝟒𝟒
𝟓𝟓
=
𝟐𝟐√𝟑𝟑
√𝟏𝟏𝟏𝟏
=
𝟖𝟖 − √ 𝟕𝟕
𝟑𝟑√ 𝟕𝟕
=
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.3.1

UNIT 02 October
𝟐𝟐 − √𝟐𝟐
𝟒𝟒 + √𝟐𝟐
=
6. Simplify
𝟓𝟓
𝟐𝟐√𝟑𝟑 − √𝟐𝟐
=
−𝟏𝟏 + 𝟑𝟑√𝟐𝟐
√𝟏𝟏𝟏𝟏 + √𝟑𝟑
=
𝟔𝟔 + √𝟐𝟐
√𝟔𝟔 + 𝟐𝟐√𝟑𝟑
=
−√𝟏𝟏𝟏𝟏
𝟐𝟐√𝟐𝟐 + √𝟔𝟔
=
7. Rationalize:
𝟖𝟖
𝟑𝟑√𝟖𝟖
𝟒𝟒 =
√𝟓𝟓 − 𝟒𝟒
√𝟔𝟔
=
𝟒𝟒
√𝟑𝟑 − 𝟓𝟓√ 𝟕𝟕
=
−𝟏𝟏
√𝟐𝟐 − √𝟓𝟓
=
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.3.2

UNIT 02 October
8. Write in Standard form:
a) Earth-Moon´s Distance: 384,000 km
b) Earth-Neptune´s Distance: 4,308,000,000 km
c) Earth Surface: 150,000,000 km2
d) A Light-year: 9,460,000,000,000 km
e) Distance from observable universe: 25,000 light-years.
9. Write in Standard form:
a) Electron´s Diameter: 0.0000000003 m.
b) Virus´ Length: 0.0000000022 m.
c) Proton´s Radius: 0.00000000005 m.
d) Staphylococcus´ Mass: 0.0000001 g.
10. Look for the Proton´s Mass and express it in standard form:
Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.3.3

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4 ESO Academics - Unit 02 - Exercises 4.2.3 - Rationalizing the Denominator and Standard Form

1. UNIT 02 October 1. Rationalize the denominator: 2. Rationalize the denominator: 3. Solve: 4. Rationalize the denominator: 5. Rationalize the denominator 𝟏𝟏 + √𝟑𝟑 𝟏𝟏 − √𝟐𝟐 = 𝟓𝟓 𝟑𝟑 − √𝟓𝟓 = √𝟓𝟓 𝟑𝟑 − √ 𝟕𝟕 = 𝟒𝟒 √ 𝟕𝟕 = −𝟔𝟔 √𝟐𝟐 𝟑𝟑 = −𝟑𝟑 √𝟐𝟐 = 𝟏𝟏𝟏𝟏 √𝟓𝟓𝟑𝟑𝟖𝟖 = −𝟐𝟐 𝟐𝟐 + √𝟔𝟔 = 𝟏𝟏 √𝟑𝟑 + √𝟓𝟓 = 𝟐𝟐 𝟑𝟑 + √𝟑𝟑 𝟒𝟒 = √𝟓𝟓 √𝟑𝟑 = 𝟓𝟓 −𝟐𝟐√ 𝟒𝟒 𝟓𝟓 = 𝟐𝟐√𝟑𝟑 √𝟏𝟏𝟏𝟏 = 𝟖𝟖 − √ 𝟕𝟕 𝟑𝟑√ 𝟕𝟕 = Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.3.1

2. UNIT 02 October 𝟐𝟐 − √𝟐𝟐 𝟒𝟒 + √𝟐𝟐 = 6. Simplify 𝟓𝟓 𝟐𝟐√𝟑𝟑 − √𝟐𝟐 = −𝟏𝟏 + 𝟑𝟑√𝟐𝟐 √𝟏𝟏𝟏𝟏 + √𝟑𝟑 = 𝟔𝟔 + √𝟐𝟐 √𝟔𝟔 + 𝟐𝟐√𝟑𝟑 = −√𝟏𝟏𝟏𝟏 𝟐𝟐√𝟐𝟐 + √𝟔𝟔 = 7. Rationalize: 𝟖𝟖 𝟑𝟑√𝟖𝟖 𝟒𝟒 = √𝟓𝟓 − 𝟒𝟒 √𝟔𝟔 = 𝟒𝟒 √𝟑𝟑 − 𝟓𝟓√ 𝟕𝟕 = −𝟏𝟏 √𝟐𝟐 − √𝟓𝟓 = Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.3.2

3. UNIT 02 October 8. Write in Standard form: a) Earth-Moon´s Distance: 384,000 km b) Earth-Neptune´s Distance: 4,308,000,000 km c) Earth Surface: 150,000,000 km2 d) A Light-year: 9,460,000,000,000 km e) Distance from observable universe: 25,000 light-years. 9. Write in Standard form: a) Electron´s Diameter: 0.0000000003 m. b) Virus´ Length: 0.0000000022 m. c) Proton´s Radius: 0.00000000005 m. d) Staphylococcus´ Mass: 0.0000001 g. 10. Look for the Proton´s Mass and express it in standard form: Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.2.3.3

4 ESO Academics - Unit 02 - Exercises 4.2.3 - Rationalizing the Denominator and Standard Form

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