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Step-by-step explanation:
1/(√7 - √6)
The denominator is √7 - √6.
We know that
Rationalising factor of √a - √b = √a + √b.
So, the rationalising factor of √7 - √6 = √7 + √6.
On comparing the denominator them
=> [1/(√7 - √6)]×[(√7 - √6)/(√7- √6)]
=> [1(√7 + √6)]/[(√7 - √6)(√7 + √6)]
Applying algebraic identity in denominator; (a-b)(a+b) = a^2 - b^2. Where, a = √7 and b = √6.
=> [1(√7 + √6)]/[(√7)^2 - (√6)^2)]
=> [1(√7 + √6)]/(7 - 6)
=> [1(√7 + √6)]/1
=> 1(√7 + √6)
=> √7 + √6
Hence, the denominator is rationalised.
→ √7 - √6
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Answers & Comments
i hope this helps
pls mark me as brainliest
Step-by-step explanation:
Solution:
1/(√7 - √6)
The denominator is √7 - √6.
We know that
Rationalising factor of √a - √b = √a + √b.
So, the rationalising factor of √7 - √6 = √7 + √6.
On comparing the denominator them
=> [1/(√7 - √6)]×[(√7 - √6)/(√7- √6)]
=> [1(√7 + √6)]/[(√7 - √6)(√7 + √6)]
Applying algebraic identity in denominator; (a-b)(a+b) = a^2 - b^2. Where, a = √7 and b = √6.
=> [1(√7 + √6)]/[(√7)^2 - (√6)^2)]
=> [1(√7 + √6)]/(7 - 6)
=> [1(√7 + √6)]/1
=> 1(√7 + √6)
=> √7 + √6
Hence, the denominator is rationalised.
Answer:
→ √7 - √6
Used Formulae: