tính
\(\sqrt{2^2.3^4}\)
Tính :
\(\sqrt{2^2.3^4}\)
\(\sqrt{2^2}3^4\)=\(\sqrt{2^2.\left(3^2\right)^2=}\)\(\sqrt{2^2}.\sqrt{9^2}=2.9=18\)
tính
a) \(\sqrt{16}.\sqrt{25}+\sqrt{196}:\sqrt{49}\)
b) 36 : \(\sqrt{2.3^2.18}-\sqrt{169}\)
c) \(\sqrt{\sqrt{81}}\)
d) \(\sqrt{3^2+4^2}\)
a: \(=4\cdot5+14:7\)
=20+2
=22
Áp dụng quy tắc khai phương một tích, hãy tính:
a. \(\sqrt{0,09.64}\)
b. \(\sqrt{2^4.\left(-7\right)^2};\)
c. \(\sqrt{12,1.360};\)
c. \(\sqrt{2^2.3^4}.\)
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) đáp án :24
b) đáp án :28
c)đáp án :66
d)đáp án:18
Áp dung quy tắc khai phương một tích,hãy tính:
a) \(\sqrt{0,09.64}\)
b) \(\sqrt{2^4.\left(-7\right)^2}\)
c) \(\sqrt{12,1.360}\)
d)\(\sqrt{2^2.3^4}\)
a) \(\sqrt{0,09.64}=\sqrt{\left(0,3\right)^2.8^2}=0,3.8=2,4\)
b) \(\sqrt{2^4.\left(-7\right)^2}=\sqrt{\left(2^2\right)^2.\left(-7\right)^2}=2^2.\left|-7\right|=7.4=28\)
c) \(\sqrt{12,1.360}=\sqrt{12,1.10.36}=\sqrt{121.36}=\sqrt{11^2.6^2}=11.6=66\)
d) \(\sqrt{2^2.3^4}=\sqrt{2^2.\left(3^2\right)^2}=2.3^2=9.2=18\)
a) \(\sqrt{0,09\cdot64}=\sqrt{0,09}\cdot\sqrt{64}=0,3\cdot8=2,4\)
b) \(\sqrt{2^4\cdot\left(-7\right)^2}=\sqrt{2^4}\cdot\sqrt{\left(-7\right)^2}=2^2\cdot7=4\cdot7=28\)
c) \(\sqrt{12,1\cdot360}=\sqrt{12,1\cdot10\cdot36}=\sqrt{121\cdot36}=\sqrt{121}\cdot\sqrt{36}=11\cdot6=66\)
d) \(\sqrt{2^2\cdot3^4}=\sqrt{2^2}\cdot\sqrt{3^4}=2\cdot3^2=2\cdot9=18\)
Tính:
a. \(\sqrt{16}.\sqrt{25}+\sqrt{196}:\sqrt{49};\)
b. \(36:\sqrt{2.3^2.18}-\sqrt{169};\)
c. \(\sqrt{\sqrt{81}};\)
d. \(\sqrt{3^2+4^2}.\)
a) \(\sqrt{16}\cdot\sqrt{25}+\sqrt{196}:\sqrt{49}\)
\(=\sqrt{16\cdot25}+\sqrt{196:49}\)
\(=20+2=22\)
b) \(36:\sqrt{2\cdot3^2\cdot18}-\sqrt{169}\)
\(=36:\sqrt{324}-\sqrt{169}\)
\(=36:18-13=2-13=-11\)
c) \(\sqrt{\sqrt{81}}\)
\(=\sqrt{9}=3\)
d) \(\sqrt{3^2+4^2}\)
\(=\sqrt{9+16}=\sqrt{25}=5\)
a) \(\sqrt{16}.\sqrt{25}+\sqrt{196}\div\sqrt{49}\)
\(=4.5+14:7\)
\(=20+2=22\)
b) \(36:\sqrt{2.3^2.18}-\sqrt{169}\)
\(=36:18-13=-11\)
c) \(\sqrt{\sqrt{81}}=\sqrt{9}=3\)
d) \(\sqrt{3^2+4^2}=\sqrt{25}=5\)
B1: tính : a, \(\sqrt{400.0,81}\)
b, \(\sqrt{\dfrac{5}{27}.\dfrac{3}{20}}\)
c, \(\sqrt{\left(-5\right)^2.3^2}\)
d, \(\sqrt{\left(2-\sqrt{5}\right)^2.\left(2+\sqrt{5}\right)^2}\)
a)\(\sqrt{400.0,81}=\sqrt{4.81}=\sqrt{2^2.9^2}=2.9=18\)
b)\(\sqrt{\dfrac{5}{27}.\dfrac{3}{20}}=\sqrt{\dfrac{5}{3^3}.\dfrac{3}{2^2.5}}=\sqrt{\dfrac{1}{3^2.2^2}}=\dfrac{1}{3.2}=\dfrac{1}{6}\)
c)\(\sqrt{\left(-5\right)^2.3^2}=\sqrt{5^2.3^2}=5.3=15\)
d)\(\sqrt{\left(2-\sqrt{5}\right)^2\left(2+\sqrt{5}\right)^2}=\sqrt{\left[2^2-\left(\sqrt{5}\right)^2\right]^2}=\sqrt{\left(-1\right)^2}=1\)
Tính \(S=\sqrt{1+\dfrac{8.1^2-1}{1^2.3^2}}+\sqrt{1+\dfrac{8.2^2-1}{3^2.5^2}}+...+\sqrt{1+\dfrac{8.n^2-1}{\left(2n-1\right)^2.\left(2n+1\right)^2}}\)
Với\(n\in N\)
Thực hiện phép tính:
\(A=\dfrac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\dfrac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(B=\dfrac{1-\dfrac{1}{\sqrt{49}}+\dfrac{1}{49}-\dfrac{1}{\left(7\sqrt{7}\right)^2}}{\dfrac{\sqrt{64}}{2}-\dfrac{4}{7}+\dfrac{2^2}{7^2}-\dfrac{4}{343}}\)
\(B=\frac{1-\frac{1}{\sqrt{49}}+\frac{1}{49}-\frac{1}{\left(7\sqrt{7}\right)^2}}{\frac{\sqrt{64}}{2}-\frac{4}{7}+\frac{2^2}{7^2}-\frac{4}{343}}\)
\(B=\frac{1-\frac{1}{7}+\frac{1}{49}-\frac{1}{343}}{\frac{8}{2}-\frac{4}{7}+\frac{4}{49}-\frac{4}{343}}\)
\(B=\frac{\frac{343}{343}-\frac{49}{343}+\frac{7}{343}-\frac{1}{343}}{4-\frac{4}{7}+\frac{28}{343}-\frac{4}{343}}\)
\(B=\frac{\frac{300}{343}}{\frac{28}{7}-\frac{4}{7}+\frac{24}{343}}\)
\(B=\frac{\frac{300}{343}}{\frac{24}{7}+\frac{24}{343}}\)
\(B=\frac{\frac{300}{343}}{\frac{1323}{343}+\frac{24}{343}}\)
\(B=\frac{300}{343}:\frac{1347}{343}\)
\(B=\frac{100}{449}\)
\(A=\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^6+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(A=\frac{2^{12}.3^5-2^{12}.3^6}{2^{12}.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^6}{5^9.7^3+5^9.2^3.7^3}\)
\(A=\frac{2^{12}.3^5\left(1-3\right)}{2^{12}.3^5.\left(3+1\right)}-\frac{5^{10}.7^3.\left(1-7^3\right)}{5^9.7^3.\left(1+8\right)}\)
\(A=\frac{-2}{4}-\frac{5.\left(-342\right)}{9}\)
\(A=\frac{-1}{2}+\frac{1710}{9}\)
\(A=\frac{-1}{2}+190\)
\(A=\frac{-1}{2}+\frac{380}{2}\)
\(A=\frac{379}{2}\)
\(A=\frac{2^{12}.3^5-4^6.9^2}{\left(2^2.3\right)^3+8^4.3^5}-\frac{5^{10}.7^3-25^5.49^2}{\left(125.7\right)^3+5^9.14^3}\)
\(A=\frac{2^{12}.3^5-\left(2^2\right)^6.\left(3^2\right)^2}{\left(2^2\right)^6.3^6+\left(2^3\right)^4.3^5}-\frac{5^{10}.7^3-\left(5^2\right)^5.\left(7^2\right)^2}{\left(5^3\right)^3.7^3+5^9.\left(2.7\right)^3}\)
\(A=\frac{2^{12}.3^5-2^{12}.3^4}{2^6.3^6+2^{12}.3^5}-\frac{5^{10}.7^3-5^{10}.7^4}{5^9.7^3+5^9.2^3.7^3}\)
\(A=\frac{2^{12}\left(3^5-3^4\right)}{2^6\left(3^6-3^5\right)}-\frac{5^{10}\left(7^3-7^4\right)}{5^9\left(7^3+2^3.7^3\right)}\)
\(A=\frac{2^6\left(3^5-3^4\right)}{3^6-3^5}-\frac{5\left(7^3-7^4\right)}{7^3+2^3.7^3}\) ( \(\frac{5\left(7^3-7^4\right)}{7^3.1+2^3.7^3}=\frac{5\left(7^3-7^4\right)}{7^3\left(1+2^3\right)}\))
\(A=\frac{2^6\left(3^5-3^4\right)}{3^6-3^5}-\frac{5\left(7^3-7^4\right)}{7^3\left(1+2^3\right)}\)
\(A=\frac{2^6.162}{486}-\frac{5.\left(-2058\right)}{7^3.9}\)
\(\Rightarrow A=\frac{648}{486}-\frac{-12540}{3087}\)
bạn tự tính nha máy tính mình mất r
Bài 17 (trang 14 SGK Toán 9 Tập 1)
Áp dụng quy tắc khai phương một tích, hãy tính:
a) $\sqrt{0,09.64}$ ; b) $\sqrt{2^4.(-7)^2}$ ;
c) $\sqrt{12,1.360}$ ; d) $\sqrt{2^2.3^4}$
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
a) .
b) .
c) .
d)