Mathematics: What is the answer for: 1÷6 + √3

What is the answer for: 1÷6 + √3 - id1634957001, quantaviousw49

Theresab2021

17.01.2022

To simplify the given expression we need to remove the radical from the denominator by rationalizing it.

To rationalize a radical expression first step is multiply both numerator and denominator of the expression by the conjugate of it's denominator.

So, conjugate of 6+√3 = 6-√3.

Hence,

$\frac{1}{6+\sqrt{3}} *\frac{6-\sqrt{3}}{6-\sqrt{3}}$

= $\frac{6-\sqrt{3}}{(6+\sqrt{3})(6-\sqrt{3})}$

= $\frac{6-\sqrt{3}}{6^2-\sqrt{3}^2}$ Since (a+b)(a-b)= a^2-b^2

= $\frac{6-\sqrt{3}}{36-3}$

= $\frac{6-\sqrt{3}}{33}$

So, the answer is $\frac{6-\sqrt{3}}{33}$

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