Math, asked by mm1651057, 1 month ago

maths
Simplify:6÷√12-√3​

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Answers

Answered by SarcasticBunny
32

Given :-

\sf \bullet \;\; \dfrac{6}{\sqrt{12} -\sqrt{3}}

To Do :-

  • Simplify

Solution :-

\sf : \; \implies \dfrac{6}{\sqrt{3 \times 2 \times 2} - \sqrt{3} }

\sf : \; \implies \dfrac{6}{ 2\sqrt{3} - \sqrt{3} }

\sf : \; \implies \dfrac{6}{ \sqrt{3} }

\sf : \; \implies \dfrac{6}{ \sqrt{3} } \times \dfrac{\sqrt{3} }{\sqrt{3} }

\sf : \; \implies \dfrac{6\sqrt{3} }{ (\sqrt{3})^{2} }

\sf : \; \implies \dfrac{6\sqrt{3} }{ 3}

\boxed{\bf{ \star \;\;  2 \sqrt{3} \;\; }}

Answered by lconic
9

Given :-

6 ÷ √12-√3​

To Find :-

Simplified Value

Solution :-

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

  • Factor 12 = 2²×3. Rewrite the square root of the product √2² × 3    as the product of square roots √2² × √3. Take the square root of 2².

\sf \dashrightarrow \; \dfrac{6}{2\sqrt{3} - \sqrt{3}}

  • Combine 2√3 and -√3 to get √3

\sf \dashrightarrow \; \dfrac{6}{ \sqrt{3}}

  • Rationalize the denominator of √3 by multiplying numerator and denominator by √3.

\sf \dashrightarrow \;  \bigg( \dfrac{6 \sqrt{3} }{ ( \sqrt{3} )^{2} }\bigg)

\sf \dashrightarrow \; \dfrac{6 \sqrt{3} }{ 3 }

\sf \dashrightarrow 2\sqrt{3}

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀

  • Henceforth, the simplified value is 2√3.

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