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Question
Find the product.
`(sqrt(2) + 3sqrt(11))(5sqrt(2) - 2sqrt(11))`
Sum
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Solution
Let’s find the product:
`(sqrt(2) + 3sqrt(11))(5sqrt(2) - 2sqrt(11))`
Use distributive property (FOIL method):
Multiply each term:
1. `sqrt(2) xx 5sqrt(2)`
= 5 × 2
= 10
2. `sqrt(2) xx (-2sqrt(11))`
= `-2sqrt(22)`
3. `3sqrt(11) xx 5sqrt(2)`
= `15sqrt(22)`
4. `3sqrt(11) xx (-2sqrt(11))`
= –6 × 11
= –66
Now combine all:
`10 - 2sqrt(22) + 15sqrt(22) - 66`
Combine like terms:
- Constants: 10 – 66 = –56
- Surds: `-2sqrt(22) + 15sqrt(22) = 13sqrt(22)`
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Chapter 1: Rational and Irrational Numbers - EXERCISE 1C [Page 15]
