Question

What would be the denominator after rationalizing 7/(5√3 – 5√2)? *

1 point

19

20

25

NONE OF THESE.​

Answer 1

$\underline{\underline{\sf{\maltese\:\:Given }}}$

$\sf \implies \dfrac{7}{(5 \sqrt{3} - 5 \sqrt{2}) }$

$\underline{\underline{\sf{\maltese\:\:To \: find }}}$

$\sf \implies Denominator \: after \: rationalising = \: ?$

$\underline{\underline{\sf{\maltese\:\:Solution }}}$

$\sf \implies \dfrac{7}{(5 \sqrt{3} - 5 \sqrt{2}) }$

On rationalising,

$\sf \implies \dfrac{7}{(5 \sqrt{3} - 5 \sqrt{2}) } \times \dfrac{5 \sqrt{3} + 5 \sqrt{2}}{5 \sqrt{3} + 5 \sqrt{2}}$

Combine the fractions,

$\sf \implies \dfrac{7(5 \sqrt{3} + 5 \sqrt{2})}{(5 \sqrt{3} - 5 \sqrt{2})(5 \sqrt{3} + 5 \sqrt{2}) }$

We know that,

$\sf \implies (a - b)(a + b) = a ^{2} - b^{2}$

So,

$\sf \implies \dfrac{7(5 \sqrt{3} + 5 \sqrt{2})}{(5 \sqrt{3})^{2} - (5 \sqrt{2})^{2} }$

$\sf \implies \dfrac{7(5 \sqrt{3} + 5 \sqrt{2})}{75 - 50 }$

$\sf \implies \dfrac{7(5 \sqrt{3} + 5 \sqrt{2})}{25 }$

$\sf \implies \dfrac{ \cancel{5}(7( \sqrt{3} + \sqrt{2}))}{ \cancel{25 }}$

$\sf \implies \dfrac{7( \sqrt{3} + \sqrt{2})}{ 5 }$

Hence after rationalising,

$\sf \implies \underline{ \boxed{ \sf We \: got \: denominator \: as \:\bf 5}} \: \: \bigstar$