g: \(=\sqrt{5a}-4\sqrt{a}+7\sqrt{a}\)

\(=\sqrt{5a}+3\sqrt{a}\)

b: \(=\dfrac{40}{6+2\sqrt{5}+2\cdot\sqrt{2+2\sqrt{5}}}\)

\(=\dfrac{40}{\left(\sqrt{5}+1\right)^2+\sqrt{2}\cdot\sqrt{4+4\sqrt{5}}}\)

\(=\dfrac{40}{\left(\sqrt{5}+1\right)^2+2\sqrt{2}\cdot\sqrt{\sqrt{5}+1}}\)

\(=\dfrac{40}{\left(\sqrt{\sqrt{5}+1}\right)\left[\left(\sqrt{\sqrt{5}+1}\right)^3+2\sqrt{2}\right]}\)

a) \(A=\sqrt{9a}-\sqrt{16a}-\sqrt{49a}=3\sqrt{a}-4\sqrt{a}-7\sqrt{a}=-8\sqrt{a}\)

b) \(B=\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{\sqrt{2}}-\left(\sqrt{3}+\sqrt{2}\right)\)

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

\(=2+\sqrt{3}+\sqrt{2}+1-\sqrt{3}-\sqrt{2}=3\)

2) \(\sqrt{98}-\sqrt{72}+0,5\sqrt{8}\)

\(=7\sqrt{2}-6\sqrt{2}+\sqrt{2}\)

\(=\left(7-6+1\right)\sqrt{2}\)

\(=2\sqrt{2}\)

3) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\)

\(=3\sqrt{a}-4\sqrt{a}+7\sqrt{a}\)

\(=\left(3-4+7\right)\sqrt{a}\)

\(=6\sqrt{a}\)

4) \(\sqrt{16b}+2\sqrt{40b}-3\sqrt{90b}\)

\(=4\sqrt{b}+4\sqrt{10b}-9\sqrt{10b}\)

\(=4\sqrt{b}-5\sqrt{10b}\)

Gấp nha 

b: B=căn 49a^2+3a

=|7a|+3a

=7a+3a(a>=0)

=10a

c: C=căn16a^4+6a^2

=4a^2+6a^2

=10a^2

d: \(D=3\cdot3\cdot\sqrt{a^6}-6a^3=6\cdot\left|a^3\right|-6a^3\)

TH1: a>=0

D=6a^3-6a^3=0

TH2: a<0

D=-6a^3-6a^3=-12a^3

e: \(E=3\sqrt{9a^6}-6a^3\)

\(=3\cdot\sqrt{\left(3a^3\right)^2}-6a^3\)

=3*3a^3-6a^3(a>=0)

=3a^3

f: \(F=\sqrt{16a^{10}}+6a^5\)

\(=\sqrt{\left(4a^5\right)^2}+6a^5\)

=-4a^5+6a^5(a<=0)

=2a^5

a: \(\dfrac{2}{\sqrt{3}-1}-\dfrac{2}{\sqrt{3}+1}\)

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

\(=\dfrac{2\sqrt{3}+2-2\sqrt{3}+2}{2}=\dfrac{4}{2}=2\)

b: \(\dfrac{\sqrt{12}-\sqrt{6}}{\sqrt{30}-\sqrt{15}}\)

\(=\dfrac{\sqrt{6}\left(\sqrt{2}-1\right)}{\sqrt{15}\left(\sqrt{2}-1\right)}\)

\(=\dfrac{\sqrt{6}}{\sqrt{15}}=\sqrt{\dfrac{6}{15}}=\sqrt{\dfrac{2}{5}}=\dfrac{\sqrt{10}}{5}\)

c: \(\sqrt{9a}+\sqrt{81a}+3\sqrt{25a}-16\sqrt{49a}\)

\(=3\sqrt{a}+9\sqrt{a}+3\cdot5\sqrt{a}-16\cdot7\sqrt{a}\)

\(=27\sqrt{a}-112\sqrt{a}=-85\sqrt{a}\)

d: \(\dfrac{ab-bc}{\sqrt{ab}-\sqrt{bc}}=\dfrac{\left(\sqrt{ab}-\sqrt{bc}\right)\left(\sqrt{ab}+\sqrt{bc}\right)}{\sqrt{ab}-\sqrt{bc}}\)

\(=\sqrt{ab}+\sqrt{bc}\)

e: \(a\left(\sqrt{\dfrac{a}{b}+2\sqrt{ab}+b\cdot\sqrt{\dfrac{a}{b}}}\right)\cdot\sqrt{ab}\)

\(=a\cdot\sqrt{\dfrac{a}{b}\cdot ab+2\sqrt{ab}\cdot ab+b\cdot\sqrt{\dfrac{a}{b}}\cdot ab}\)

\(=a\cdot\sqrt{a^2+2\cdot ab\cdot\sqrt{ab}+a\sqrt{a}\cdot b\sqrt{b}}\)

\(=a\cdot\sqrt{a^2+3\cdot a\cdot\sqrt{a}\cdot b\cdot\sqrt{b}}\)

e: ĐKXĐ: a>=0 và a<>1

\(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right)\cdot\dfrac{1+a\sqrt{a}}{1+\sqrt{a}}\)

\(=\left(\dfrac{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}+a\right)}{1-\sqrt{a}}+\sqrt{a}\right)\cdot\dfrac{\left(\sqrt{a}+1\right)\left(a-\sqrt{a}+1\right)}{\sqrt{a}+1}\)

\(=\left(1+\sqrt{a}+\sqrt{a}+a\right)\cdot\left(a-\sqrt{a}+1\right)\)

\(=\left(\sqrt{a}+1\right)^2\cdot\left(a-\sqrt{a}+1\right)\)

1) \(\sqrt{9a}-\sqrt{16a}+\sqrt{49a}\left(a\ge0\right)\)\(=3\sqrt{a}-4\sqrt{a}+7\sqrt{a}\) \(=6\sqrt{a}\)

2) \(2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{80}}\)

= \(2\sqrt{80\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{5}}\)

= \(8\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{5}}\)

= \(6\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{5}}\)

3) \(\dfrac{\sqrt{x^3}-1}{\sqrt{x}-1}\) = \(\dfrac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}-1}\) = \(x+\sqrt{x}+1\)

\(P=5\sqrt{a}+7\sqrt{a}-8\sqrt{a}=4\sqrt{a}\\ Q=\left[2+\dfrac{\sqrt{a}\left(\sqrt{a}+1\right)}{\sqrt{a}+1}\right]\left[2-\dfrac{\sqrt{a}\left(\sqrt{a}-1\right)}{\sqrt{a}-1}\right]\\ Q=\left(2+\sqrt{a}\right)\left(2-\sqrt{a}\right)=4-a\)