18/10 + 6/38=
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\(\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\)
\(=\sqrt{7-2\sqrt{21}+3}+\sqrt{7+2\sqrt{21}+3}\)
\(=\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}\right)^2+2.\sqrt{7}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\)
\(=\left|\sqrt{7}-\sqrt{3}\right|+\left|\sqrt{7}+\sqrt{3}\right|\)
\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)
\(=\sqrt{7}+\sqrt{7}=2\sqrt{7}\)
Ta có: \(\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\)
\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)
\(=2\sqrt{7}\)
10/29+11/29+12/29+...+19/29
=10+11+12+13+14+15+=16+17+18+19/29
=145/29
\(=\sqrt{7-2\sqrt{21}+3}+\sqrt{7+2\sqrt{21}+3}\)
\(=\sqrt{\sqrt{7}^2-2\sqrt{7}.\sqrt{3}+\sqrt{3}^2}+\sqrt{\sqrt{7}^2+2\sqrt{7}.\sqrt{3}+\sqrt{3}^2}\)
\(=\sqrt{\left(\sqrt{7}-\sqrt{3}\right)^2}+\sqrt{\left(\sqrt{7}+\sqrt{3}\right)^2}\)
\(=\left|\sqrt{7}-\sqrt{3}\right|+\left|\sqrt{7}+\sqrt{3}\right|\)
\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)
\(=2\sqrt{7}\)
\(\sqrt{10-2\sqrt{21}}+\sqrt{10+2\sqrt{21}}\)
\(=\sqrt{7}-\sqrt{3}+\sqrt{7}+\sqrt{3}\)
\(=2\sqrt{7}\)
\(a\)) \(\left(4^2.4^3\right):2^{10}\)
\(=4^5:2^{10}\)
\(=\left(2^2\right)^5:2^{10}\)
\(=2^{10}:2^{10}\)
\(=1\)
\(b\)) \(\left(0,6\right)^5:\left(0,2\right)^6\)
\(=\left(\frac{3}{5}\right)^5:\left(\frac{1}{5}\right)^6\)
\(=\frac{3^5}{5^5}:\frac{1^6}{5^6}\)
\(=\frac{3^5}{5^5}.5^6\)
\(=\frac{3^5.5^6}{5^5}\)
\(=3^5.5\)
\(=243.5\)
\(=1215\)
\(c\)) \(\left(2^7.9^3\right):\left(6^5.8^2\right)\)
\(=\left[2^7.\left(3^2\right)^3\right]:\left[\left(2.3\right)^5.\left(2^4\right)^2\right]\)
\(=\left(2^7.3^6\right):\left[2^5.3^5.2^8\right]\)
\(=\left(2^7.3^6\right).\left(\frac{1}{2^5.3^5.2^8}\right)\)
\(=\frac{2^7.3^6.1}{\left(2^5.2^8\right).3^5}\)
\(=\frac{2^7.3^6}{2^{13}.3^5}\)
\(=\frac{3}{2^6}\)
\(=\frac{3}{64}\)
a: =1/2(3/4+1)=1/2x7/4=7/8
b: =9/8-1/6=27/24-4/24=23/24
bang 15
18/10 + 6/38
= 342/190 + 30/190
= 372/190
= 186/95