To simplify the problem, just distribute the radical to each term in the parentheses. 

$\displaystyle \\\sqrt{3}(\sqrt{3}+4)\\=\sqrt{9}+4\sqrt{3}\\=3+4\sqrt{3}$

To simplify the problem, just distribute the radical to each term in the parentheses. 

$\displaystyle \\\sqrt{3}(\sqrt{7}+\sqrt{12})\\=\sqrt{21}+\sqrt{36}\\=\sqrt{21}+6$

To simplify the problem, just distribute the radical to each term in the parentheses. 

$\displaystyle \\-\sqrt{6}(\sqrt{5}-\sqrt{2})\\=-\sqrt{30}+\sqrt{12}\\=-\sqrt{30}+2\sqrt{3}$

To simplify the problem, just distribute the radical to each term in the parentheses. 

$\displaystyle \\-2\sqrt{5}(7\sqrt{3}+3\sqrt{10})\\=-14\sqrt{15}-6\sqrt{50}$

$\displaystyle \\-14\sqrt{15}-6\sqrt{50}\\=-14\sqrt{15}-6*5\sqrt{2}\\=-14\sqrt{15}-30\sqrt{2}$

 $\displaystyle (\sqrt{2}+\sqrt{7})(\sqrt{27}+\sqrt{12})$ 

Let's simplify the right parentheses.

$\displaystyle (\sqrt{27}+\sqrt{12})=(3\sqrt{{3}}+2\sqrt{3})=5\sqrt{3}$ 

Now we can distribute the radical to each term in the parentheses.

$\displaystyle 5\sqrt{3}(\sqrt{2}+\sqrt{7})=5\sqrt{6}+5\sqrt{21}$

Square both sides:

x = (3²)² = 9² = 81

To simplify, break down each square root into its component factors:

$\displaystyle \sqrt{507}+\sqrt{12}$

$\displaystyle \sqrt{169\cdot 3}+\sqrt{4\cdot 3}$

$\displaystyle \sqrt{13\cdot13\cdot3}\:+\sqrt{2\cdot 2\cdot 3}$

You can remove pairs of factors and bring them outside the square root sign. At this point, since each term shares $\displaystyle \sqrt3$, you can add them together to yield the final answer:

$\displaystyle 13\sqrt{3}+2\sqrt{3}=15\sqrt{3}$

Take each fraction separately first:

(2√3)/(√2) = [(2√3)/(√2)] * [(√2)/(√2)] = (2 * √3 * √2)/(√2 * √2) = (2 * √6)/2 = √6

Similarly:

(4√2)/(√3) = [(4√2)/(√3)] * [(√3)/(√3)] = (4√6)/3 = (4/3)√6

Now, add them together:

√6 + (4/3)√6 = (3/3)√6 + (4/3)√6 = (7/3)√6

Begin by factoring out each of the radicals:

$\displaystyle \sqrt{60}+\sqrt{40}+\sqrt{10}=\sqrt{4*15}+\sqrt{4*10}+\sqrt{10}$

For the first two radicals, you can factor out a $\displaystyle \sqrt{4}$ or $\displaystyle 2$:

$\displaystyle 2\sqrt{15}+2\sqrt{10}+\sqrt{10}$

The other root values cannot be simply broken down. Now, combine the factors with $\displaystyle \sqrt{10}$:

$\displaystyle 2\sqrt{15}+2\sqrt{10}+\sqrt{10}=2\sqrt{15}+3\sqrt{10}$

This is your simplest form.

Begin by getting your $\displaystyle x$ terms onto the left side of the equation and your numeric values onto the right side of the equation:

$\displaystyle 15\sqrt{x}-4\sqrt{x}=4+10$

Next, you can combine your radicals. You do this merely by subtracting their respective coefficients:

$\displaystyle 11\sqrt{x}=14$

Now, square both sides:

$\displaystyle (11\sqrt{x})^2=(14)^2$

$\displaystyle (11)^2(\sqrt{x})^2=(14)^2$

$\displaystyle 121x=196$

Solve by dividing both sides by $\displaystyle 121$:

$\displaystyle x=\frac{196}{121}$