Question

root 7 minus root 5 by root 7 + root 5 rationalise the denominator with steps and explanation
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Answer 1

Answer:

27 - 7√5/22

Step-by-step explanation:

7-√5/7+√5

Rationalizing the denominator by multiplying both the numerator and the denominator by the reciprocal of the denominator :

= 7-√5/7+√5 x 7-√5/7-√5

= 7-√5)^2/(7)^2 - (√5)^2

Now, at the numerator,

As we know,

(a-b)^2

=a^2 - 2ab + b^2

And,

At the denominator,

As we know,

(a+b)(a-b)

= a^2 - b^2

Therefore,

7-√5)^2/(7)^2 - (√5)^2

= (7)^2-2(7)(√5)+(√5)^2/49-5

= 49 - 14√5 + 5/44

= 49+5 - 14√5/44

=54 - 14√5/44

= 2(27-7√5)/44

= 27 - 7√5/22