\(a=\sqrt{\left(6,8-3,2\right)\left(6,8+3,2\right)}=\sqrt{3,6\left(10\right)}=\sqrt{36}=6\)

a) \(\sqrt{6,8^2-3,2^2}=\sqrt{\left(6,8-3,2\right)\left(6,8+3,2\right)}\)

=\(\sqrt{3,6.10}=\sqrt{36}=6\)

b)\(\sqrt{21,8^2-18,2^2}=\sqrt{\left(21,8-18,2\right)\left(21,8+18,2\right)}\)

=\(\sqrt{3,6.40}=\sqrt{144}=12\)

c)\(\sqrt{117,5^2-26,5^2-1440}=\sqrt{\left(117,5-26,5\right)\left(117,5+26,5\right)-1440}\)

=\(\sqrt{91.144-1440}=\sqrt{144.81}=\sqrt{144}.\sqrt{81}=108\)

d)\(\sqrt{146,5^2-109,5^2+27.256}\)=\(\sqrt{\left(146,5-109,5\right)\left(146,5+109,5\right)+27.256}\)

=\(\sqrt{37.256+\sqrt{27.256}}=\sqrt{64.256}=\sqrt{64}.\sqrt{256}=128\)

\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\frac{\sqrt{0,5}.\sqrt{25}}{\sqrt{0,5}}=\sqrt{25}=5\)

\(\frac{\sqrt{6}}{\sqrt{150}}=\frac{\sqrt{6}}{\sqrt{6}.\sqrt{25}}=\frac{1}{\sqrt{25}}=\frac{1}{5}\)

\(\sqrt{6,8^2-3,2^2}=\sqrt{\left(6,8+3,2\right)\left(6,8-3,2\right)}=\sqrt{10.3,6}=\sqrt{36}=6\)

\(\sqrt{21,8^2-18,2^2}=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}=\sqrt{40.3,6}=\sqrt{144}=12\)

\(\frac{\sqrt{12,5}}{\sqrt{0,5}}=\sqrt{\frac{12,5}{0,5}}=\sqrt{25}=5\)

\(\frac{\sqrt{6}}{\sqrt{150}}=\sqrt{\frac{6}{150}}=\sqrt{\frac{1}{25}}=\frac{1}{5}\)

\(\sqrt{\left(6,8\right)^2-\left(3,2\right)^2}=\sqrt{46,24-10,24}=\sqrt{36}=6\)

\(\sqrt{\left(21,8\right)^2-\left(18,2\right)^2}=\sqrt{475,24-331,24}=\sqrt{144}=12\)

\(a,\sqrt{68^2-32^2}\)

\(=\sqrt{\left(68-32\right)\left(68+32\right)}\)

\(=\sqrt{3600}=60\)

\(b,\sqrt{37^2-12^2}\)

\(=\sqrt{\left(37-12\right)\left(37+12\right)}\)

\(=\sqrt{25.49}=5.7=35\)

\(c,\sqrt{21,8^2-18,2^2}\)

\(=\sqrt{\left(21,8+18,2\right)\left(21,8-18,2\right)}\)

\(=\sqrt{40.3,6}=12\)

1,

\(a,=\sqrt{\left(21,8-18,2\right)\left(21,8+18,2\right)}\\ =\sqrt{3,6\cdot40}\\ =\sqrt{36\cdot4}\\ =\sqrt{36}\cdot\sqrt{4}\\ =6\cdot4\\ =24\)

\(b,=10\cdot\sqrt{\left(6,5-1,6\right)\left(6,5+1,6\right)}\\ =10\cdot\sqrt{4,9\cdot8,1}\\ =10\cdot\sqrt{49\cdot0,81}\\ =10\cdot\sqrt{49}\cdot\sqrt{0,81}\\ =10\cdot7\cdot0,9\\ =63\)

2,

\(A=7+4\sqrt{3}+\sqrt{3}-1\\ =6+5\sqrt{3}\\ B=7+2\sqrt{10}-\left(11+2\sqrt{10}\right)\\ =7+2\sqrt{10}-11-2\sqrt{10}\\ =-4\)

Lời giải:

$\sqrt{6,8^2-3,2^2}=\sqrt{(6,8-3,2)(6,8+3,2)}=\sqrt{3,6.10}=\sqrt{36}=6$

a) \({4^6}.\sqrt {0,1}  = 1295,2689\)

b) \(\sqrt[8]{{2,{1^{18}} + 1}} - \sqrt {2,{1^{12}} + 1}  =  - 80,4632\)

c) \(\frac{{1,{5^3}}}{{\sqrt[3]{{6,8}}}} = 1,7814\)