9.5 Addition and subtraction of square root expressions

$4\sqrt{18}-5\sqrt{8}$

$6x\sqrt{48}+8x\sqrt{75}$

$-7\sqrt{84x}-12\sqrt{189x}+2\sqrt{21x}$

$9\sqrt{6}-8\sqrt{6}+3$

$\sqrt{a^3}+4a\sqrt{a}$

$4x\sqrt{54x^3}+\sqrt{36x^2}+3\sqrt{24x^5}-3x$

$\sqrt{5}\left(\sqrt{6}-4\right)$

$\left(\sqrt{5}+\sqrt{7}\right)\left(\sqrt{2}+\sqrt{8}\right)$

$\left(3\sqrt{2}-2\sqrt{3}\right)\left(4\sqrt{3}+\sqrt{8}\right)$

$\frac{4+\sqrt{5}}{3-\sqrt{8}}$

$4\sqrt{5}-2\sqrt{5}$

$10\sqrt{2}+8\sqrt{2}$

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

$-\sqrt{10}-2\sqrt{10}$

$3\sqrt{7x}+2\sqrt{7x}$

$6\sqrt{3a}+\sqrt{3a}$

$2\sqrt{18}+5\sqrt{32}$

$4\sqrt{27}-3\sqrt{48}$

$\sqrt{200}-\sqrt{128}$

$4\sqrt{300}+2\sqrt{500}$

$6\sqrt{40}+8\sqrt{80}$

$2\sqrt{120}-5\sqrt{30}$

$8\sqrt{60}-3\sqrt{15}$

$\sqrt{a^3}-3a\sqrt{a}$

$\sqrt{4x^3}+x\sqrt{x}$

$2b\sqrt{a^3{b}^5}+6a\sqrt{a{b}^7}$

$5xy\sqrt{2x{y}^3}-3y^2\sqrt{2x^{3}y}$

$5\sqrt{20}+3\sqrt{45}-3\sqrt{40}$

$\sqrt{24}-2\sqrt{54}-4\sqrt{12}$

$6\sqrt{18}+5\sqrt{32}+4\sqrt{50}$

$-8\sqrt{20}-9\sqrt{125}+10\sqrt{180}$

$2\sqrt{27}+4\sqrt{3}-6\sqrt{12}$

$\sqrt{14}+2\sqrt{56}-3\sqrt{136}$

$3\sqrt{2}+2\sqrt{63}+5\sqrt{7}$

$4ax\sqrt{3x}+2\sqrt{3a^2{x}^3}+7\sqrt{3a^2{x}^3}$

$3by\sqrt{5y}+4\sqrt{5b^2{y}^3}-2\sqrt{5b^2{y}^3}$

$\sqrt{2}\left(\sqrt{3}+1\right)$

$\sqrt{3}\left(\sqrt{5}-3\right)$

$\sqrt{5}\left(\sqrt{3}-\sqrt{2}\right)$

$\sqrt{7}\left(\sqrt{6}-\sqrt{3}\right)$

$\sqrt{8}\left(\sqrt{3}+\sqrt{2}\right)$

$\sqrt{10}\left(\sqrt{10}-\sqrt{5}\right)$

$\left(1+\sqrt{3}\right)\left(2-\sqrt{3}\right)$

$\left(5+\sqrt{6}\right)\left(4-\sqrt{6}\right)$

$\left(3-\sqrt{2}\right)\left(4-\sqrt{2}\right)$

$\left(5+\sqrt{7}\right)\left(4-\sqrt{7}\right)$

$\left(\sqrt{2}+\sqrt{5}\right)\left(\sqrt{2}+3\sqrt{5}\right)$

$\left(2\sqrt{6}-\sqrt{3}\right)\left(3\sqrt{6}+2\sqrt{3}\right)$

$\left(4\sqrt{5}-2\sqrt{3}\right)\left(3\sqrt{5}+\sqrt{3}\right)$

$\left(3\sqrt{8}-2\sqrt{2}\right)\left(4\sqrt{2}-5\sqrt{8}\right)$

$\left(\sqrt{12}+5\sqrt{3}\right)\left(2\sqrt{3}-2\sqrt{12}\right)$

${\left(1+\sqrt{3}\right)}^2$

${\left(3+\sqrt{5}\right)}^2$

${\left(2-\sqrt{6}\right)}^2$

${\left(2-\sqrt{7}\right)}^2$

${\left(1+\sqrt{3x}\right)}^2$

${\left(2+\sqrt{5x}\right)}^2$

${\left(3-\sqrt{3x}\right)}^2$

${\left(8-\sqrt{6b}\right)}^2$

${\left(2a+\sqrt{5a}\right)}^2$

${\left(3y-\sqrt{7y}\right)}^2$

$\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)$

$\left(2+\sqrt{5}\right)\left(2-\sqrt{5}\right)$

$\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)$

$\left(6+\sqrt{7}\right)\left(6-\sqrt{7}\right)$

$\left(\sqrt{2}+\sqrt{3}\right)\left(\sqrt{2}-\sqrt{3}\right)$

$\left(\sqrt{5}+\sqrt{2}\right)\left(\sqrt{5}-\sqrt{2}\right)$

$\left(\sqrt{a}+\sqrt{b}\right)\left(\sqrt{a}-\sqrt{b}\right)$

$\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)$

$\frac{2}{5+\sqrt{3}}$

$\frac{4}{6+\sqrt{2}}$

$\frac{1}{3-\sqrt{2}}$

$\frac{1}{4-\sqrt{3}}$

$\frac{8}{2-\sqrt{6}}$

$\frac{2}{3-\sqrt{7}}$

$\frac{\sqrt{5}}{3+\sqrt{3}}$

$\frac{\sqrt{3}}{6+\sqrt{6}}$

$\frac{2-\sqrt{8}}{2+\sqrt{8}}$

$\frac{4+\sqrt{5}}{4-\sqrt{5}}$

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

$\frac{8-\sqrt{3}}{2+\sqrt{18}}$

$\frac{6-\sqrt{2}}{4+\sqrt{12}}$

$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

$\frac{\sqrt{6a}-\sqrt{8a}}{\sqrt{8a}+\sqrt{6a}}$

$\frac{\sqrt{2b}-\sqrt{3b}}{\sqrt{3b}+\sqrt{2b}}$

( [link] ) Simplify ${\left(\frac{x^5{y}^3}{x^{2}y}\right)}^5.$

( [link] ) Simplify ${\left(8x^{3}y\right)}^2{\left(x^2{y}^3\right)}^4.$

( [link] ) Write ${\left(x-1\right)}^4{\left(x-1\right)}^{-7}$ so that only positive exponents appear.

( [link] ) Simplify $\sqrt{27x^5{y}^{10}{z}^3.}$

( [link] ) Simplify $\frac{1}{2+\sqrt{x}}$ by rationalizing the denominator.