Bài 1 Rút gọn (Đưa thừa số ra ngoài dấu căn nếu được)
a)Căn 98 – Căn 72 + 0,5 Căn 8
b)2 Căn 8 – Căn 12 + 3 Căn 2
c)Căn 5 + Căn 20 – Căn 10
d)Căn 9a – Căn 10a – Căn 49a ()
e)Căn 160 + 2 Căn 40b – 3 Căn 90b ()
f)( 2 Căn 3 + Căn 5). Căn 3 – Căn 60
g)(Căn 28 – Căn 12 – Căn 7)(Căn 7 + 2 Căn 21)
Đáp án:
$a)
2\sqrt{2}\\
b)
7\sqrt{2}-2\sqrt{3}\\
c)
3\sqrt{5}-\sqrt{10}\\
d)
\sqrt{a}\left ( -4-\sqrt{10} \right )\\
e)
\sqrt{10}\left ( 4-5\sqrt{b} \right )\\
f)
6-\sqrt{15}\\
g)
7+14\sqrt{3}-2\sqrt{21}-12\sqrt{7}$
Giải thích các bước giải:
$a)
\sqrt{98}-\sqrt{72}+0,5\sqrt{8}=\sqrt{7^2.2}-\sqrt{6^2.2}+\dfrac{1}{2}\sqrt{2^3}\\
=7\sqrt{2}-6\sqrt{2}+\dfrac{1}{2}.2\sqrt{2}=2\sqrt{2}\\
b)
2\sqrt{8}-\sqrt{12}+3\sqrt{2}=2\sqrt{2^3}-\sqrt{2^2.3}+3\sqrt{2}\\
=2.2\sqrt{2}-2\sqrt{3}+3\sqrt{2}=7\sqrt{2}-2\sqrt{3}\\
c)
\sqrt{5}+\sqrt{20}-\sqrt{10}=\sqrt{5}+\sqrt{2^2.5}-\sqrt{10}\\
=\sqrt{5}+2\sqrt{5}-\sqrt{10}=3\sqrt{5}-\sqrt{10}\\
d)
\sqrt{9a}-\sqrt{10a}-\sqrt{49a}=\sqrt{3^2a}-\sqrt{10a}-\sqrt{7^2a}\\
=3\sqrt{a}-\sqrt{10}.\sqrt{a}-7\sqrt{a}\\
=-4\sqrt{a}-\sqrt{10}.\sqrt{a}\\
=\sqrt{a}\left ( -4-\sqrt{10} \right )\\
e)
\sqrt{160}+2\sqrt{40b}-3\sqrt{90b}\\
=\sqrt{4^2.10}+2\sqrt{2^2.10b}-3\sqrt{3^2.10b}\\
=4\sqrt{10}+2.2\sqrt{10b}-3.3\sqrt{10b}\\
=4\sqrt{10}-5\sqrt{10b}\\
=\sqrt{10}\left ( 4-5\sqrt{b} \right )\\
f)
\left ( 2\sqrt{3}+\sqrt{5} \right ).\sqrt{3}-\sqrt{60}\\
=2\sqrt{3}.\sqrt{3}+\sqrt{3}.\sqrt{5}-\sqrt{2^2.15}\\
=6+\sqrt{15}-2\sqrt{15}\\
=6-\sqrt{15}\\
g)
\left ( \sqrt{28}-\sqrt{12}-\sqrt{7} \right ).\left ( \sqrt{7}+2\sqrt{21} \right )\\
=\left ( \sqrt{2^2.7}-\sqrt{2^2.3}-\sqrt{7} \right ).\left ( \sqrt{7}+2\sqrt{21} \right )\\
=\left ( 2\sqrt{7}-2\sqrt{3}-\sqrt{7} \right ).\left ( \sqrt{7}+2\sqrt{21} \right )\\
=2.\sqrt{7}\sqrt{7}+4\sqrt{7}\sqrt{21}-2\sqrt{3}\sqrt{7}-2\sqrt{3}.2\sqrt{21}-\sqrt{7}\sqrt{7}-\sqrt{7}.2\sqrt{21}\\
=2.7+4.7\sqrt{3}-2\sqrt{21}-4.3\sqrt{7}-7-7.2\sqrt{3}\\
=14+28\sqrt{3}-2\sqrt{21}-12\sqrt{7}-7-14\sqrt{3}\\
=7+14\sqrt{3}-2\sqrt{21}-12\sqrt{7}$