a) \(\sqrt{90\cdot6.4}=\sqrt{9\cdot10\cdot6,4}=\sqrt{9\cdot64}=\sqrt{9}\cdot\sqrt{64}=3\cdot8=24\)

b)\(\sqrt{2,5\cdot14,4}=\sqrt{25\cdot144\cdot\frac{1}{100}}=\sqrt{25}\cdot\sqrt{144}\cdot\sqrt{\frac{1}{100}}=5\cdot12\cdot\frac{1}{10}=6\)

thank bn

a, \(\sqrt{0.09\cdot64=\sqrt{0.09}\cdot\sqrt{64}=0.3\cdot8=2.4}\)

b, \(\sqrt{2^4\cdot\left(-7\right)^2}=\sqrt{16\cdot49}=\sqrt{16}\cdot\sqrt{49}=4\cdot7=28\)

c, \(\sqrt{121\cdot360}=\sqrt{121\cdot36}=\sqrt{121}\cdot\sqrt{36}=11\cdot6=66\)

d, \(\sqrt{2^2\cdot3^4}=\sqrt{2^2}\cdot\sqrt{3^4}=2\cdot3^2=18\)

a)\(\sqrt{0,09}.\sqrt{64}\)=0,3.8=2,4

b)\(\sqrt{2^4}.\sqrt{\left(-7\right)^2}\)=4.7=28

c)\(\sqrt{121.36}\)=\(\sqrt{121}.\sqrt{36}\)=11.6=66

d)\(\sqrt{2^2}.\sqrt{3^4}\)=2.9=18

\(\sqrt{7+4\sqrt{3}}=\sqrt{\left(2+\sqrt{3}\right)^2}=2+\sqrt{3}\)

\(\sqrt{8-2\sqrt{12}}=\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}=\left|\sqrt{6}-\sqrt{2}\right|=\sqrt{6}-\sqrt{2}\)

\(\sqrt{21+6\sqrt{6}}=\sqrt{\left(3\sqrt{2}-\sqrt{3}\right)^2}=\left|3\sqrt{2}-\sqrt{3}\right|=3\sqrt{2}-\sqrt{3}\)

\(\sqrt{15-6\sqrt{6}}=\sqrt{\left(3-\sqrt{6}\right)^2}=\left|3-\sqrt{6}\right|=3-\sqrt{6}\)

\(\sqrt{29-12\sqrt{5}}=\sqrt{\left(2\sqrt{5}-3\right)^2}=\left|2\sqrt{5}-3\right|=2\sqrt{5}-3\)

\(\sqrt{41+12\sqrt{5}}=\sqrt{\left(6+\sqrt{5}\right)^2}=6+\sqrt{5}\)

a) ĐS: 2.4.

b) ĐS: 28.

c) HD: Đổi 12,1.360 thành 121.36. ĐS: 66

d) ĐS: 18.

a) \(\sqrt{0,09.64}\)

\(=\sqrt{0,09}.\sqrt{64}\)

\(=0,3.8=2,4\)

b) \(\sqrt{2^4.\left(-7\right)^2}\)

\(=\sqrt{2^4}.\sqrt{\left(-7\right)^2}\)

\(=2^2.7=4.7=28\)

c) \(\sqrt{12,1.360}\)

\(=\sqrt{121.36}\)

\(=\sqrt{121}.\sqrt{36}\)

\(=11.6=66\)

d) \(\sqrt{2^2.3^4}\)

\(=\sqrt{2^2}.\sqrt{3^4}\)

\(=2.3^2=2.9=18\)

a)\(\sqrt{75\cdot48}=\sqrt{25\cdot3\cdot48}=\sqrt{25\cdot144}=\sqrt{25}\cdot\sqrt{144}=5\cdot12=60\)

b) \(\sqrt{2,5\cdot14,4}=\sqrt{25\cdot144\cdot\frac{1}{100}}=\sqrt{25}\cdot\sqrt{144}\cdot\sqrt{\frac{1}{100}}=5\cdot12\cdot\frac{1}{10}=6\)

a)\(\sqrt{45.80}=\sqrt{9.400}=\sqrt{9}.\sqrt{400}=3.20=60\)

b) \(\sqrt{75.48}=\sqrt{25.3.16.3}=\sqrt{5^2.3^2.4^2}=5.4.3=60\)

c)\(\sqrt{90.6,4}=\sqrt{10.9.4.1,6}=\sqrt{4^2.3^2.2^2}=4.3.2=24\)

d) \(\sqrt{2,5.14,4}=\sqrt{\dfrac{25}{10}.\dfrac{144}{10}}=\sqrt{\dfrac{25.144}{100}}=\sqrt{\left(\dfrac{5.12}{10}\right)^2}=\dfrac{5.12}{10}=6\)

a) \(\sqrt{45.80}=\sqrt{9.400}=\sqrt{9}.\sqrt{400}=3.20=60\)

b)\(\sqrt{75.48}=\sqrt{25.3.3.16}=5.3.4=60\)

c)\(\sqrt{90.6,4}=\sqrt{9.64}=3.8=24\)

d)\(\sqrt{2,5.14,4}=\sqrt{\dfrac{25}{10}.\dfrac{144}{10}}=\sqrt{\dfrac{25.144}{100}=\dfrac{5.12}{10}=\dfrac{60}{10}=6}\)

 Có \(\left(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\right)^2\)

\(=\left(\sqrt{17-3\sqrt{32}}\right)^2+2\left(\sqrt{17-3\sqrt{32}}\right)\left(\sqrt{17+3\sqrt{32}}\right)\)\(+\left(\sqrt{17=3\sqrt{32}}\right)^2\)

 \(=17-3\sqrt{32}+2\sqrt{\left(17-3\sqrt{32}\right)\left(17+3\sqrt{32}\right)}\)\(+17+3\sqrt{32}\)

\(=34+2\sqrt{17^2-9.32}\)

\(=34+2\sqrt{289-288}\)

\(=34+2\sqrt{1}=34+2=36\)

\(\Rightarrow\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)

\(=\sqrt{36}=6\)

(Vì có \(\hept{\begin{cases}\sqrt{17-3\sqrt{32}}\ge0\\\sqrt{17+3\sqrt{32}}\ge0\end{cases}}\)nên \(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\ge0\))

Ở cuối dòng 2 mình nhầm dấu + thành dấu = nghe mọi người