Ответы к странице 130
498. Вычислите значение выражения:
1) $sqrt{9 * 25}$;
2) $sqrt{16 * 2500}$;
3) $sqrt{0,64 * 36}$;
4) $sqrt{400 * 1,44}$;
5) $sqrt{0,09 * 0,04}$;
6) $sqrt{6,25 * 0,16}$;
7) $sqrt{6^2 * 3^4}$;
8) $sqrt{7^2 * 2^8}$;
9) $sqrt{25 * 64 * 0,36}$;
10) $sqrt{0,01 * 0,81 * 2500}$;
11) $sqrt{frac{81}{100}}$;
12) $sqrt{frac{49}{256}}$;
13) $sqrt{3frac{13}{36}}$;
14) $sqrt{3frac{1}{16} * 2frac{14}{25}}$;
15) $sqrt{frac{169}{36 * 81}}$;
16) $sqrt{frac{121 * 256}{25 * 100}}$.
Решение:
1) $sqrt{9 * 25} = sqrt{9} * sqrt{25} = 3 * 5 = 15$
2) $sqrt{16 * 2500} = sqrt{16} * sqrt{2500} = 4 * 50 = 200$
3) $sqrt{0,64 * 36} = sqrt{0,64} * sqrt{36} = 0,8 * 6 = 4,8$
4) $sqrt{400 * 1,44} = sqrt{400} * sqrt{1,44} = 20 * 1,2 = 24$
5) $sqrt{0,09 * 0,04} = sqrt{0,09} * sqrt{0,04} = 0,3 * 0,2 = 0,06$
6) $sqrt{6,25 * 0,16} = sqrt{6,25} * sqrt{0,16} = 2,5 * 0,4 = 1$
7) $sqrt{6^2 * 3^4} = sqrt{6^2} * sqrt{3^4} = sqrt{6^2} * sqrt{(3^2)^2} = |6| * |3^2| = 6 * 9 = 54$
8) $sqrt{7^2 * 2^8} = sqrt{7^2} * sqrt{(2^4)^2} = |7| * |2^4| = 7 * 16 = 112$
9) $sqrt{25 * 64 * 0,36} = sqrt{25} * sqrt{64} * sqrt{0,36} = 5 * 8 * 0,6 = 40 * 0,6 = 24$
10) $sqrt{0,01 * 0,81 * 2500} = sqrt{0,01} * sqrt{0,81} * sqrt{2500} = 0,1 * 0,9 * 50 = 0,9 * 5 = 4,5$
11) $sqrt{frac{81}{100}} = frac{sqrt{81}}{sqrt{100}} = frac{9}{10} = 0,9$
12) $sqrt{frac{49}{256}} = frac{sqrt{49}}{sqrt{256}} = frac{7}{16}$
13) $sqrt{3frac{13}{36}} = sqrt{frac{121}{36}} = frac{sqrt{121}}{sqrt{36}} = frac{11}{6} = 1frac{5}{6}$
14) $sqrt{3frac{1}{16} * 2frac{14}{25}} = sqrt{frac{49}{16} * frac{64}{25}} = sqrt{frac{49}{16}} * sqrt{frac{64}{25}} = frac{sqrt{49}}{sqrt{16}} * frac{sqrt{64}}{sqrt{25}} = frac{7}{4} * frac{8}{5} = frac{7}{1} * frac{2}{5} = frac{14}{5} = 2frac{4}{5}$
15) $sqrt{frac{169}{36 * 81}} = frac{sqrt{169}}{sqrt{36} * sqrt{81}} = frac{sqrt{169}}{sqrt{36 * 81}} = frac{13}{6 * 9} = frac{13}{54}$
16) $sqrt{frac{121 * 256}{25 * 100}} = frac{sqrt{121 * 256}}{sqrt{25 * 100}} = frac{sqrt{121} * sqrt{256}}{sqrt{25} * sqrt{100}} = frac{11 * 16}{5 * 10} = frac{11 * 8}{5 * 5} = frac{88}{25} = 3frac{13}{25} $
499. Чему равно значение выражения:
1) $sqrt{36 * 81}$;
2) $sqrt{900 * 49}$;
3) $sqrt{16 * 0,25}$;
4) $sqrt{9 * 1,69}$;
5) $sqrt{0,36 * 1,21}$;
6) $sqrt{5^2 * 3^6}$;
7) $sqrt{4^4 * 3^2}$;
8) $sqrt{2^6 * 5^2}$;
9) $sqrt{2,25 * 0,04 * 1600}$;
10) $sqrt{13frac{4}{9}}$;
11) $sqrt{1frac{7}{9} * frac{4}{25}}$;
12) $sqrt{frac{1}{16} * frac{9}{25}}$?
Решение:
1) $sqrt{36 * 81} = sqrt{36} * sqrt{81} = 6 * 9 = 54$
2) $sqrt{900 * 49} = sqrt{900} * sqrt{49} = 30 * 7 = 210$
3) $sqrt{16 * 0,25} = sqrt{16} * sqrt{0,25} = 4 * 0,5 = 2$
4) $sqrt{9 * 1,69} = sqrt{9} * sqrt{1,69} = 3 * 1,3 = 3,9$
5) $sqrt{0,36 * 1,21} = sqrt{0,36} * sqrt{1,21} = 0,6 * 1,1 = 0,66$
6) $sqrt{5^2 * 3^6} = sqrt{5^2} * sqrt{3^6} = sqrt{5^2} * sqrt{(3^3)^2} = |5| * |3^3| = 5 * |27| = 5 * 27 = 135$
7) $sqrt{4^4 * 3^2} = sqrt{4^4} * sqrt{3^2} = sqrt{(4^2)^2} * sqrt{3^2} = |4^2| * |3| = |16| * 3 = 16 * 3 = 48$
8) $sqrt{2^6 * 5^2} = sqrt{2^6} * sqrt{5^2} = sqrt{(2^3)^2} * sqrt{5^2} = |2^3| * |5| = |8| * 5 = 8 * 5 = 40$
9) $sqrt{2,25 * 0,04 * 1600} = sqrt{2,25} * sqrt{0,04} * sqrt{1600} = 1,5 * 0,2 * 40 = 0,3 * 40 = 12$
10) $sqrt{13frac{4}{9}} = sqrt{frac{121}{9}} = frac{sqrt{121}}{sqrt{9}} = frac{11}{3} = 3frac{2}{3}$
11) $sqrt{1frac{7}{9} * frac{4}{25}} = sqrt{frac{16}{9}} * sqrt{frac{4}{25}} = frac{sqrt{16}}{sqrt{9}} * frac{sqrt{4}}{sqrt{25}} = frac{4}{3} * frac{2}{5} = frac{8}{15}$
12) $sqrt{frac{1}{16} * frac{9}{25}} = sqrt{frac{1}{16}} * sqrt{frac{9}{25}} = frac{sqrt{1}}{sqrt{16}} * frac{sqrt{9}}{sqrt{25}} = frac{1}{4} * frac{3}{5} = frac{3}{20}$
500. Найдите значение выражения:
1) $sqrt{12} * sqrt{3}$;
2) $sqrt{32} * sqrt{2}$;
3) $sqrt{18} * sqrt{50}$;
4) $sqrt{0,009} * sqrt{1000}$;
5) $sqrt{200} * sqrt{0,18}$;
6) $sqrt{13} * sqrt{2} * sqrt{26}$;
7) $sqrt{2,4} * sqrt{1frac{2}{3}}$;
8) $sqrt{frac{2}{11}} * sqrt{8} * sqrt{frac{1}{11}}$;
9) $sqrt{2^3 * 3} * sqrt{2^5 * 3^3}$.
Решение:
1) $sqrt{12} * sqrt{3} = sqrt{12 * 3} = sqrt{36} = 6$
2) $sqrt{32} * sqrt{2} = sqrt{32 * 2} = sqrt{64} = 8$
3) $sqrt{18} * sqrt{50} = sqrt{18 * 50} = sqrt{900} = 30$
4) $sqrt{0,009} * sqrt{1000} = sqrt{0,009 * 1000} = sqrt{9} = 3$
5) $sqrt{200} * sqrt{0,18} = sqrt{200 * 0,18} = sqrt{36} = 6$
6) $sqrt{13} * sqrt{2} * sqrt{26} = sqrt{13 * 2 * 26} = sqrt{26 * 26} = sqrt{26^2} = |26| = 26$
7) $sqrt{2,4} * sqrt{1frac{2}{3}} = sqrt{2,4 * 1frac{2}{3}} = sqrt{frac{24}{10} * frac{5}{3}} = sqrt{frac{12}{5} * frac{5}{3}} = sqrt{frac{4}{1} * frac{1}{1}} = sqrt{4} = 2$
8) $sqrt{frac{2}{11}} * sqrt{8} * sqrt{frac{1}{11}} = sqrt{frac{2}{11} * 8 * frac{1}{11}} = sqrt{frac{16}{11^2}} = frac{4}{|11|} = frac{4}{11}$
9) $sqrt{2^3 * 3} * sqrt{2^5 * 3^3} = sqrt{2^3 * 3 * 2^5 * 3^3} = sqrt{2^{3 + 5} * 3^{1 + 3}} = sqrt{2^{8} * 3^{4}} = sqrt{2^{8}} * sqrt{3^{4}} = sqrt{(2^4)^2} * sqrt{(3^2)^2} = |2^4| * |3^2| = |16| * |9| = 144$
501. Найдите значение выражения:
1) $sqrt{27} * sqrt{3}$;
2) $sqrt{18} * sqrt{2}$;
3) $sqrt{10} * sqrt{12,1}$;
4) $sqrt{0,5} * sqrt{50}$;
5) $sqrt{1frac{3}{7}} * sqrt{2,8}$;
6) $sqrt{5 * 2^3} * sqrt{5^3 * 2^3}$.
Решение:
1) $sqrt{27} * sqrt{3} = sqrt{27 * 3} = sqrt{81} = 9$
2) $sqrt{18} * sqrt{2} = sqrt{18 * 2} = sqrt{36} = 6$
3) $sqrt{10} * sqrt{12,1} = sqrt{10 * 12,1} = sqrt{121} = 11$
4) $sqrt{0,5} * sqrt{50} = sqrt{0,5 * 50} = sqrt{25} = 5$
5) $sqrt{1frac{3}{7}} * sqrt{2,8} = sqrt{1frac{3}{7} * 2,8} = sqrt{frac{10}{7} * frac{28}{10}} = sqrt{frac{1}{1} * frac{4}{1}} = sqrt{4} = 2$
6) $sqrt{5 * 2^3} * sqrt{5^3 * 2^3} = sqrt{5 * 2^3 * 5^3 * 2^3} = sqrt{5^{1 + 3} * 2^{3 + 3}} = sqrt{5^{4} * 2^{6}} = sqrt{5^4} * sqrt{2^{6}} = sqrt{(5^2)^2} * sqrt{(2^3)^2} = |5^2| * |2^3| = |25| * |8| = 25 * 8 = 200$
502. Найдите значение выражения:
1) $frac{sqrt{75}}{sqrt{3}}$;
2) $frac{sqrt{98}}{sqrt{2}}$;
3) $frac{sqrt{3}}{sqrt{48}}$;
4) $frac{sqrt{3,2}}{sqrt{0,2}}$;
5) $frac{sqrt{72}}{sqrt{50}}$;
6) $frac{sqrt{27}}{sqrt{147}}$;
7) $frac{sqrt{6} * sqrt{3}}{sqrt{2}}$;
8) $frac{sqrt{5}}{sqrt{3} * sqrt{15}}$.
Решение:
1) $frac{sqrt{75}}{sqrt{3}} = sqrt{frac{75}{3}} = sqrt{25} = 5$
2) $frac{sqrt{98}}{sqrt{2}} = sqrt{frac{98}{2}} = sqrt{49} = 7$
3) $frac{sqrt{3}}{sqrt{48}} = sqrt{frac{3}{48}} = sqrt{frac{1}{16}} = frac{1}{4}$
4) $frac{sqrt{3,2}}{sqrt{0,2}} = sqrt{frac{3,2}{0,2}} = sqrt{frac{32}{2}} = sqrt{16} = 4$
5) $frac{sqrt{72}}{sqrt{50}} = sqrt{frac{72}{50}} = sqrt{frac{36}{25}} = frac{6}{5} = 1frac{1}{5}$
6) $frac{sqrt{27}}{sqrt{147}} = sqrt{frac{27}{147}} = sqrt{frac{9}{49}} = frac{3}{7}$
7) $frac{sqrt{6} * sqrt{3}}{sqrt{2}} = frac{sqrt{6 * 3}}{sqrt{2}} = frac{sqrt{18}}{sqrt{2}} = sqrt{frac{18}{2}} = sqrt{9} = 3$
8) $frac{sqrt{5}}{sqrt{3} * sqrt{15}} = frac{sqrt{5}}{sqrt{3 * 15}} = frac{sqrt{5}}{sqrt{45}} = sqrt{frac{5}{45}} = sqrt{frac{1}{9}} = frac{1}{3}$