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 \(\displaystyle 121\):

\(\displaystyle x=\frac{196}{121}\)

Let us factor 108 and 81

\(\displaystyle 108=2\times 54= 2\times 2\times 27= 2^2\times 3\times 9= 2^2\times 3^2\times 3\)

\(\displaystyle 81=9\times 9=9^2\)

\(\displaystyle \sqrt{108}-\sqrt{81}=6\sqrt{3}-9\)

√27 is the same as 3√3, while √12 is the same as 2√3.

3√3 + 2√3 = 5√3

(5√3)/(√3) = 5

When dividing square roots, we divide the numbers inside the radical. Simplify if necessary.

\(\displaystyle \frac{\sqrt{210}}{\sqrt{6}}=\frac{\sqrt{35}*\sqrt{6}}{\sqrt{6}}=\sqrt{35}\)