Question

3√5-√7/3√3+√2 , Simplify the given number by rationalising the denominator.

Answer 1

Given (3√5-√7)/(3√3 + √2)

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

=[9√15-3√10-3√21+√14]/[(3√3)²-(√2)²]

[ Since x²-y² =(x+y)(x-y)]

=[9√15-3√10-3√21+√14]/(27-2)

= (9√15-3√10-3√21+√14)/25

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Answer 2

Answer:

$=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{25}$        

Step-by-step explanation:

Given : Expression $\frac{3\sqrt{5}-\sqrt{7}}{3\sqrt{3}+\sqrt{2}}$

To find : Simplify the given number by rationalizing the denominator?

Solution :

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

Rationalizing the denominator by multiplying and dividing denominator by opposite sign,

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

$=\frac{(3\sqrt{5}-\sqrt{7})(3\sqrt{3}-\sqrt{2})}{(3\sqrt{3})^2-(\sqrt{2})^2}$

$=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{27-2}$

$=\frac{9\sqrt{15}-3\sqrt{10}-3\sqrt{21}+\sqrt{14}}{25}$