Question

07. Simplify the following by rationalizing the denominator

$\frac{5 \sqrt{3 + \sqrt{8} } }{7 \sqrt{2 - \sqrt{3} } }$

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Answer 1

Step-by-step explanation:

Correction :-

(5√3+√8)/(7√2-√3)

Given :-

(5√3+√8)/(7√2-√3)

To find :-

Simplify the following by rationalising the denominator ?

Solution :-

Given that

(5√3+√8)/(7√2-√3)

The denominator = 7√2-√3

The Rationalising factor of 7√2-√3 is 7√2+√3

On Rationalising the denominator then

=> [(5√3+√8)/(7√2-√3)] × [ (7√2+√3)/(7√2+√3)]

=> [5√3+√8)(7√2+√3)]×[(7√2-√3)(7√2+√3)]

=> [(5√3)(7√2)+(√8)(7√2)+(5√3)(√3)+(√8)(√3)] / [(7√2)²-(√3)²]

Since (a+b)(a-b) = a²-b²

=> (35√6+28+15+√24)/(98-3)

=> (35√6+43+2√6)/95

=> (37√6+43)/95

=> (43+37√6)/95

Answer:-

The simplification of the given problem is (43+37√6)/95

Used Formulae :-

→ (a+b)(a-b) = a²-b²

→ The Rationalising factor of√a+√b is √a-√b.