show that : 1/3-√8 - 1/√8-√7 + 1/√7-√6 -1/√6-√5 + 1/√5-2 = 5
Answers
Step-by-step explanation:
Given:-
What to do:-
1st we Rationalise all the denominator.
2nd we arrange all according to the given question and simplify and last we get the answer.
Solution:-
We have,
Now,
Rationalising each term:
The denominator is 3-√8. Multiplying the numerator and denomination by 3+√8, we get
⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator
We get,
The denominator is √8-√7. Multiplying the numerator and denomination by √8+√7, we get
⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator
We get,
The denominator is √7-√6. Multiplying the numerator and denomination by √7+√6, we get
⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator
We get,
The denominator is √6-√5. Multiplying the numerator and denomination by √6+√5, we get
⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator
We get,
The denominator is √5-2. Multiplying the numerator and denomination by √5+2, we get
⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator
We get,
Now, arranging all the rationalised denominator according to the given question and simplify that.
Hence, we showed that L.H.S = R.H.S.
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