Question

Q no 2 in attached photo

Answer 1

Answer:

answer is2√3

Step-by-step explanation:

6/√12-√3

=6(√12+√3)/12-3

=6√12+6√3/9

=12√3+6√3/9

=18√3/9=2√3(ans)

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Answer 2

Answer:

$\dfrac{6}{\sqrt{12}-\sqrt{3}}=2\sqrt{3}\quad \left(\mathrm{Decimal:\quad }\:3.46410\dots \right)$

Step-by-step explanation:

$\dfrac{6}{\sqrt{12}-\sqrt{3}}$

$\textrm{Let's simpify }\sqrt{12}$

$\mathrm{Prime\:factorization\:of\:}12:\quad 2^2\cdot \:3$

$=\sqrt{2^2\cdot \:3}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}$

$=\sqrt{3}\sqrt{2^2}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a^n}=a$

$\sqrt{2^2}=2$

$=2\sqrt{3}$

$=\dfrac{6}{2\sqrt{3}-\sqrt{3}}$

$\mathrm{Add\:similar\:elements:}\:2\sqrt{3}-\sqrt{3}=\sqrt{3}$

$=\dfrac{6}{\sqrt{3}}$

$\mathrm{Factor}\:6:\quad 2\cdot \:3$

$\mathrm{Factor}\:6:\quad 2\cdot \:3$

$\mathrm{Cancel\:}\dfrac{2\cdot \:3}{\sqrt{3}}$

$\dfrac{2\cdot \:3}{\sqrt{3}}$

$\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{a}=a^{\dfrac{1}{n}}$

$\sqrt{3}=3^{\dfrac{1}{2}}$

$=\dfrac{2\cdot \:3}{3^{\dfrac{1}{2}}}$

$\mathrm{Apply\:exponent\:rule}:\quad \dfrac{x^a}{x^b}=x^{a-b}$

$\dfrac{3^1}{3^{\dfrac{1}{2}}}=3^{1-\dfrac{1}{2}}$

$=2\cdot \:3^{-\dfrac{1}{2}+1}$

$\mathrm{Subtract\:the\:numbers:}\:1-\dfrac{1}{2}=\dfrac{1}{2}$

$=2\cdot \:3^{\dfrac{1}{2}}$

$\mathrm{Apply\:radical\:rule}:\quad \:a^{\dfrac{1}{n}}=\sqrt[n]{a}$

$3^{\dfrac{1}{2}}=\sqrt{3}$

$=2\sqrt{3}$