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प्रश्न
Write the simplest rationalising factor of `sqrt(7) - sqrt(5)`.
सोपे रूप द्या
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उत्तर
When a surd is multiplied by another surd to obtain a rational number, it is called rationalisation. Each surd is called the rationalising factor of the other.
Given, `sqrt(7) - sqrt(5)`
If we multiply `sqrt(7) - sqrt(5)` with `sqrt(7) + sqrt(5)` we will get
`(sqrt(7) - sqrt(5))(sqrt(7) + sqrt(5))`
= `(sqrt(7))^2 - (sqrt(5))^2`
= 7 – 5
= 2
→ rational number
Hence, `sqrt(7) + sqrt(5)` is the rationalising factor of `sqrt(7) - sqrt(5)`.
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