Câu hỏi của Plant vs zombies 2

Question

Rút gọn căn.

a) $\sqrt{\left|1-\sqrt{3}\right|^2}\cdot\sqrt{4+2\sqrt{3}}$

b) $2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}$

Phước Lộc · Accepted Answer

a) $\sqrt{\left|1-\sqrt{3}\right|^2}\cdot\sqrt{4+2\sqrt{3}}$

$=\sqrt{\left(\sqrt{3}-1\right)^2}\cdot\sqrt{3+2\sqrt{3}+1}$

$=\left(\sqrt{3}-1\right)\sqrt{\left(\sqrt{3}+1\right)^2}$

$=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)$

$=\left(\sqrt{3}\right)^2-1^2=3-1=2$

b) $2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}$

$=2\sqrt{40\cdot2\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{5\cdot4\sqrt{3}}$

$=2\sqrt{80\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}$

$=8\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}=0$Câu trả lời: a) $\sqrt{\left|1-\sqrt{3}\right|^2}\cdot\sqrt{4+2\sqrt{3}}$

$=\sqrt{\left(\sqrt{3}-1\right)^2}\cdot\sqrt{3+2\sqrt{3}+1}$

$=\left(\sqrt{3}-1\right)\sqrt{\left(\sqrt{3}+1\right)^2}$

$=\left(\sqrt{3}-1\right)\left(\sqrt{3}+1\right)$

$=\left(\sqrt{3}\right)^2-1^2=3-1=2$

b) $2\sqrt{40\sqrt{12}}-2\sqrt{\sqrt{75}}-3\sqrt{5\sqrt{48}}$

$=2\sqrt{40\cdot2\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{5\cdot4\sqrt{3}}$

$=2\sqrt{80\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20\sqrt{3}}$

$=8\sqrt{5\sqrt{3}}-2\sqrt{5\sqrt{3}}-6\sqrt{5\sqrt{3}}=0$

Trần Thị Kim Ngân · Answer

a) √∣∣1−√3∣∣2⋅√4+2√3|1−3|2⋅4+23

=√(√3−1)2⋅√3+2√3+1=(3−1)2⋅3+23+1

=(√3−1)√(√3+1)2=(3−1)(3+1)2

=(√3−1)(√3+1)=(3−1)(3+1)

=(√3)2−12=3−1=2=(3)2−12=3−1=2

b) 2√40√12−2√√75−3√5√4824012−275−3548

=2√40⋅2√3−2√5√3−3√5⋅4√3=240⋅23−253−35⋅43

=2√80√3−2√5√3−3√20√3=2803−253−3203

=8√5√3−2√5√3−6√5√3=0Câu trả lời: a) √∣∣1−√3∣∣2⋅√4+2√3|1−3|2⋅4+23

=√(√3−1)2⋅√3+2√3+1=(3−1)2⋅3+23+1

=(√3−1)√(√3+1)2=(3−1)(3+1)2

=(√3−1)(√3+1)=(3−1)(3+1)

=(√3)2−12=3−1=2=(3)2−12=3−1=2

b) 2√40√12−2√√75−3√5√4824012−275−3548

=2√40⋅2√3−2√5√3−3√5⋅4√3=240⋅23−253−35⋅43

=2√80√3−2√5√3−3√20√3=2803−253−3203

=8√5√3−2√5√3−6√5√3=0