Question

Rationalize the denominator 1/2√7+3√3​

Answer 1

Answer:

• 2√7 + 3√3

Explanation:

Given fraction,

$\longrightarrow \: \dfrac{1}{2 \sqrt{7 }+ 3 \sqrt{3} }$

Rationalising the denominator by multiplying the given fraction by the conjugate of the denominator i.e., 2√7 - 3√3

$\longrightarrow \: \dfrac{1}{2 \sqrt{7 }+ 3 \sqrt{3} } \times \dfrac{2 \sqrt{7} - 3 \sqrt{3} }{2 \sqrt{7} - 3 \sqrt{3} }$

$\longrightarrow \: \dfrac{1({2 \sqrt{7 }+ 3 \sqrt{3}) } } {{(2 \sqrt{7} + 3 \sqrt{3})( }{2 \sqrt{7} - 3 \sqrt{3} ) } }$

Applying the identity (a + b)(a - b) = a² - b² in the denominator.

$\longrightarrow \: \dfrac{({2 \sqrt{7 }+ 3 \sqrt{3}) } } {{(2 \sqrt{7} {)}^{2} - (3 \sqrt{3} {)}^{2} }}$

$\longrightarrow \: \dfrac{({2 \sqrt{7 }+ 3 \sqrt{3}) } } {{28- 27}}$

$\longrightarrow \: \dfrac{({2 \sqrt{7 }+ 3 \sqrt{3}) } } {{1}}$

$\longrightarrow \: {({2 \sqrt{7 }+ 3 \sqrt{3}) } }$

Required answer: 2√7 + 3√3

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Answer 2

Answer:

maybe my intentions were not to help ya.

Step-by-step explanation:

hope it helps you.