1.

Rationlise the denominator :- 2÷7+4√3​

Answer»

→{\sf{\pink{\underline{Rationalizing \:the\:denominator}}}} : when we have the denominator of a FRACTION as an IRRATIONAL , we need to convert it into a rational number by MULTIPLYING with a particular number. This is called rationalizing the denominator .

Here the denominator is (7 + 4√3) so in order to rationalise , we will multiply and divide by the opposite sign i,e ( 7 - 4√3)

As we multiply and divide simultaneously , it doesn't EFFECT the ORIGINAL value.

So we have,

= >\frac{2}{7 + 4 \sqrt{3} } \\ \\ = > \frac{2}{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ = > \frac{2(7 - 4 \sqrt{3}) }{(7) {}^{2} - (4 \sqrt{3}) {}^{2} } = \frac{14 - 8 \sqrt{3} }{49 - 48} \\ \\ = > \frac{14 - 8 \sqrt{3} }{1}

= 14 - 8√3

•°• {\bold{\underline{\underline{The\:Rationalized \:value\:is}}}} → 14 - 8√3

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