Question

va rog frumos ajutatima la toate

Answer 1

1. a) $2 \sqrt{8}=2 \sqrt{2 ^{2}*2 }=2 \sqrt{ 2^{2} } \sqrt{2}=2*2 \sqrt{2}=4 \sqrt{2}$
b) $5 \sqrt{12}=5 \sqrt{2 ^{2}*3 }=5 \sqrt{ 2^{2} } \sqrt{3}=5*2 \sqrt{3}=10 \sqrt{3}$
c) $2 \sqrt{18}=2 \sqrt{3 ^{2}*2 }=2 \sqrt{ 3^{2} } \sqrt{2}=2*3 \sqrt{2}=6 \sqrt{2}$
d) $3 \sqrt{24}=3 \sqrt{2 ^{2}*6 }=3 \sqrt{ 2^{2} } \sqrt{6}=3*2 \sqrt{6}=6 \sqrt{6}$
e) $4 \sqrt{27}=4 \sqrt{3 ^{2}*3 }=4 \sqrt{ 3^{2} } \sqrt{3}=4*3 \sqrt{3}=12 \sqrt{3}$
f) $2 \sqrt{32}=2 \sqrt{4 ^{2}*2 }=2 \sqrt{ 4^{2} } \sqrt{2}=2*4 \sqrt{2}=8 \sqrt{2}$
g) $5 \sqrt{54}=5 \sqrt{3 ^{2}*6 }=5 \sqrt{ 3^{2} } \sqrt{6}=5*3 \sqrt{6}=15 \sqrt{6}$
h) $3 \sqrt{80}=3 \sqrt{4 ^{2}*5 }=3 \sqrt{ 4^{2} } \sqrt{5}=3*4 \sqrt{5}=12 \sqrt{5}$
i) $2 \sqrt{108}=2 \sqrt{6 ^{2}*3 }=2 \sqrt{ 6^{2} } \sqrt{3}=2*6 \sqrt{3}=12 \sqrt{3}$
j) $5 \sqrt{216}=5 \sqrt{6 ^{2}*6 }=5 \sqrt{ 6^{2} } \sqrt{6}=5*6 \sqrt{6}=30 \sqrt{6}$
k) $2 \sqrt{294}=2 \sqrt{7 ^{2}*6 }=2 \sqrt{ 7^{2} } \sqrt{6}=2*7 \sqrt{6}=14 \sqrt{6}$
l) $2 \sqrt{720}=2 \sqrt{12 ^{2}*5 }=2 \sqrt{ 12^{2} } \sqrt{5}=2*12 \sqrt{5}=24 \sqrt{5}$
m) $3 \sqrt{450}=3 \sqrt{15 ^{2}*2 }=3 \sqrt{ 15^{2} } \sqrt{2}=3*15 \sqrt{2}=45 \sqrt{2}$
n) $3 \sqrt{2368}=3 \sqrt{8 ^{2}*37 }=3 \sqrt{ 8^{2} } \sqrt{37}=3*8 \sqrt{37}=24 \sqrt{37}$
o) $3 \sqrt{72 x^{6 }y ^{3} }=3*6 x^{3}y \sqrt{2y}=18 x^{3}y \sqrt{2y}$
p) $3 \sqrt{432 x^{3}y }=3*12 x \sqrt{3xy}=36 x \sqrt{3xy}$
q) $5 \sqrt{768 x^{4 }y ^{4} }=5*16 \sqrt{3} x^{2} y^{2} =80 \sqrt{3} x^{2} y^{2}$
r) $2 \sqrt{450 x^{7 } }=2*15 x^{3}\sqrt{2x}=30 x^{3} \sqrt{2x}$
s) $6 \sqrt{72 x^{8 } }=6*6 \sqrt{2} x^{4} =36 \sqrt{2} x^{4}$

2. a) $2 \sqrt{3}=3.4641$
b) $5 \sqrt{6}=12.24745$
c) $12 \sqrt{2}=16.97056$
d) $13 \sqrt{2}=18.38478$
e) $14 \sqrt{6}=34.29286$
f) $9 \sqrt{3}=15.58846$
g) $15 \sqrt{5}=33.54102$
h) $7 \sqrt{22}=23.21637$
i) $2 x^{2} \sqrt{5}=2 \sqrt{5} x^{2}$
j) $5xy \sqrt{6}=5 \sqrt{6}xy$
k) $8 x^{3} \sqrt{7}=8 \sqrt{7} x^{3}$
l) $21x y^{2} \sqrt{2}=21 \sqrt{2}x y^{2}$
m) $17 x^{4} \sqrt{5}=17 \sqrt5} x^{4}$
n) $14x y^{3} \sqrt{2}=14 \sqrt{2}x y^{3}$

3. a) $13 \sqrt{20}+255 \sqrt{45}-12 \sqrt{80}- \sqrt{125}+17 \sqrt{180}-18 \sqrt{245}=$$26 \sqrt{5}+765 \sqrt{5}-48 \sqrt{5}-5 \sqrt{5}+102 \sqrt{5}-126 \sqrt{5}=$$(26+765-48-5+102-126) \sqrt{5}=714 \sqrt{5}$
b) $16 \sqrt{28}+18 \sqrt{63}-15 \sqrt{112}-23 \sqrt{175}+ \sqrt{252}-19 \sqrt{343}=$$32 \sqrt{7}+54 \sqrt{7}-60 \sqrt{7}-115 \sqrt{7}+6 \sqrt{7}-133 \sqrt{7}=$$(32+54-60-115+6-113) \sqrt{7}=-216\sqrt{7}$
c) $21 \sqrt{44}+12 \sqrt{99}-17 \sqrt{176}-18 \sqrt{275}- \sqrt{396}-13 \sqrt{275}=$$42 \sqrt{11}+36 \sqrt{11}-68\sqrt{11}-90 \sqrt{11}\sqrt{11}-6\sqrt{11}-65 \sqrt{11}=$$(42+36-68-90-7-65) \sqrt{11}=-151\sqrt{11}$
d) $14 \sqrt{18}-16 \sqrt{72}+15 \sqrt{50}+18 \sqrt{200}- \sqrt{648}-22 \sqrt{800}=$$42 \sqrt{2}-96 \sqrt{2}+75 \sqrt{2}+180 \sqrt{2}-18 \sqrt{2}-440 \sqrt{2}=$$(42-96+75+180-18-440) \sqrt{2}=-257\sqrt{2}$
e) $16\sqrt{48}-18 \sqrt{108}-19 \sqrt{147}+17 \sqrt{12}+ 13\sqrt{75}-14 \sqrt{81}=$$64 \sqrt{3}-108 \sqrt{3}-133 \sqrt{3}+34\sqrt{3}+65 \sqrt{3}-14*9=$$-78 \sqrt{3}-126$
f) $14\sqrt{52}-18 \sqrt{117}- \sqrt{832}+17 \sqrt{117}- 19\sqrt{468}-12 \sqrt{325}=$$28 \sqrt{13}-54 \sqrt{13}-8 \sqrt{13}+51 \sqrt{13}-114 \sqrt{13}-60 \sqrt{13}=$$(28-54-8+51-114-60) \sqrt{13}=-157\sqrt{13}$