Bài 18. Áp dụng quy tắc nhân các căn bậc hai, hãy tính:
a) \(\sqrt{7}.\sqrt{63}\); b) \(\sqrt{2,5}.\sqrt{30}.\sqrt{48}\);
c) \(\sqrt{0,4}.\sqrt{6,4}\); d) \(\sqrt{2,7}.\sqrt{5}.\sqrt{1,5}\).
Hướng dẫn giải:
a)
\(\sqrt{7}.\sqrt{63}=\sqrt{7.63}=\sqrt{7.7.9}=\sqrt{7^2.3^2}=7.3=21\)
b)
\(\sqrt{2,5}.\sqrt{30}.\sqrt{48}=\sqrt{2,5.30.48}\)
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\(=\sqrt{25.3.16.3}=\sqrt{5^2.3^2.4^2}=5.3.5=60\)
c)
\(\sqrt{0,4}.\sqrt{6,4}=\sqrt{0,4.6,4}\)
\(=\sqrt{0,04.64}=\sqrt{(0,2)^2.8^2}=8.0,2=1,6\)
d)
\(\sqrt{2,7}.\sqrt{5}.\sqrt{1,5}=\sqrt{2,7.5.1,5}\)
\(=\sqrt{27.5.0,15}=\sqrt{9.3.3.0,25}\)
\(=9.0,5=4,5\)