Rút gọn căn thức
√(8+2 √(15)) – √(5)
√(10-2 √(21)) + √(3)
√(14+6 √(5)) – √(2)
√(8- √(28)) +1
Rút gọn căn thức √(8+2 √(15)) – √(5) √(10-2 √(21)) + √(3) √(14+6 √(5)) – √(2) √(8- √(28)) +1
By Camila
By Camila
Rút gọn căn thức
√(8+2 √(15)) – √(5)
√(10-2 √(21)) + √(3)
√(14+6 √(5)) – √(2)
√(8- √(28)) +1
$\sqrt{8+2\sqrt{15}}-\sqrt{5}=-\sqrt{3}\\ \sqrt{10-2\sqrt{21}}+\sqrt{3}=\sqrt{7}\\ \sqrt{14+6\sqrt{5}}-\sqrt{2}=\sqrt{9}+\sqrt{5}-\sqrt{2}\\ \sqrt{8-\sqrt{28}}+1=\sqrt{7} $
$$ ————– $$
$\sqrt{8+2\sqrt{15}}-\sqrt{5}\\ =\sqrt{5+2.\sqrt{5}.\sqrt{3}+3}-\sqrt{5}\\ =\sqrt{\left (\sqrt{5}+\sqrt{3}\right)^2}-\sqrt{5}\\ =\left |\sqrt{5}-\sqrt{3}\right |-\sqrt{5}\\ =\sqrt{5}-\sqrt{3}-\sqrt{5}\\ =\left (\sqrt{5}-\sqrt{5}\right )-\sqrt{3}\\ =-\sqrt{3}\\ \sqrt{10-2\sqrt{21}}+\sqrt{3}\\ =\sqrt{7-2.\sqrt{7}.\sqrt{3}+3}+\sqrt{3}\\ =\sqrt{\left (\sqrt{7}-\sqrt{3}\right )^2}+\sqrt{3}\\ =\left |\sqrt{7}-\sqrt{3}\right |+\sqrt{3}\\ =\sqrt{7}-\sqrt{3}+\sqrt{3}\\ =\sqrt{7}+\left (-\sqrt{3}+\sqrt{3}\right )\\ =\sqrt{7}\\ \sqrt{14+6\sqrt{5}}-\sqrt{2}\\ =\sqrt{9+2.\sqrt{9}.\sqrt{5}+5}-\sqrt{2}\\ =\sqrt{\left (\sqrt{9}+\sqrt{5}\right )^2}-\sqrt{2}\\ =\left |\sqrt{9}+\sqrt{5}\right |-\sqrt{2}\\ =\sqrt{9}+\sqrt{5}-\sqrt{2}\\ \sqrt{8-\sqrt{28}}+1\\ =\sqrt{7-2.\sqrt{7}.\sqrt{1}+1}+1\\ =\sqrt{\left (\sqrt{7}-1\right )^2}+1\\ =\left |\sqrt{7}-1\right |+1\\ =\sqrt{7}-1+1\\ =\sqrt{7}+\left (-1+1\right )\\ =\sqrt{7} $
Đáp án:
\(\sqrt{8+2\sqrt{15}}-\sqrt{5}=-\sqrt{3}\\ \sqrt{10-2\sqrt{21}}+\sqrt{3}=\sqrt{7}\\ \sqrt{14+6\sqrt{5}}-\sqrt{2}=\sqrt{9}+\sqrt{5}-\sqrt{2}\\ \sqrt{8-\sqrt{28}}+1=\sqrt{7}\)
Giải thích các bước giải:
\(\sqrt{8+2\sqrt{15}}-\sqrt{5}\\ =\sqrt{5+2.\sqrt{5}.\sqrt{3}+3}-\sqrt{5}\\ =\sqrt{\left (\sqrt{5}+\sqrt{3}\right)^2}-\sqrt{5}\\ =\left |\sqrt{5}-\sqrt{3}\right |-\sqrt{5}\\ =\sqrt{5}-\sqrt{3}-\sqrt{5}\\ =\left (\sqrt{5}-\sqrt{5}\right )-\sqrt{3}\\ =-\sqrt{3}\\ \sqrt{10-2\sqrt{21}}+\sqrt{3}\\ =\sqrt{7-2.\sqrt{7}.\sqrt{3}+3}+\sqrt{3}\\ =\sqrt{\left (\sqrt{7}-\sqrt{3}\right )^2}+\sqrt{3}\\ =\left |\sqrt{7}-\sqrt{3}\right |+\sqrt{3}\\ =\sqrt{7}-\sqrt{3}+\sqrt{3}\\ =\sqrt{7}+\left (-\sqrt{3}+\sqrt{3}\right )\\ =\sqrt{7}\\ \sqrt{14+6\sqrt{5}}-\sqrt{2}\\ =\sqrt{9+2.\sqrt{9}.\sqrt{5}+5}-\sqrt{2}\\ =\sqrt{\left (\sqrt{9}+\sqrt{5}\right )^2}-\sqrt{2}\\ =\left |\sqrt{9}+\sqrt{5}\right |-\sqrt{2}\\ =\sqrt{9}+\sqrt{5}-\sqrt{2}\\ \sqrt{8-\sqrt{28}}+1\\ =\sqrt{7-2.\sqrt{7}.\sqrt{1}+1}+1\\ =\sqrt{\left (\sqrt{7}-1\right )^2}+1\\ =\left |\sqrt{7}-1\right |+1\\ =\sqrt{7}-1+1\\ =\sqrt{7}+\left (-1+1\right )\\ =\sqrt{7}\)
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