Question

Calculati:a)4√11-7√13+3√13-5√11;b)(2√3-5√2+3)-(4√3-5√2+1);c)(-3√5)x(-2√5); d)√150+√54;e)√10+√40;f)3√48-2√108+4√300;g)(-4√12):(-2√3);h)(12√32):(4√2).

Answer 1

a)
$4 \sqrt{11}-7 \sqrt{13}+3 \sqrt{13}-5 \sqrt{11} = \\ =- \sqrt{11}-4 \sqrt{13}$

b)
$(2 \sqrt{3}-5 \sqrt{2}+3)-(4 \sqrt{3}-5 \sqrt{2}+1)= \\ 2 \sqrt{3}-5 \sqrt{2}+3- 4\sqrt{3}+5 \sqrt{2}+1=-2 \sqrt{3} +4$

c) $(-3 \sqrt{5})*(-2 \sqrt{5})=6*5=30$

d) $\sqrt{150}+ \sqrt{54}= \sqrt{2*3*5*5}+ \sqrt{2*3*3*3}=5 \sqrt{6} +3 \sqrt{6}=8 \sqrt{6}$

e)
$\sqrt{10}+ \sqrt{40}= \sqrt{10}+ \sqrt{2^{2}*2*5}= \sqrt{10}+ 2 \sqrt{10}=3 \sqrt{10}$

f)
 $3 \sqrt{48}-2 \sqrt{108}+4 \sqrt{300}= \\ 3 *4 \sqrt{3} -2*6 \sqrt{3}+4*10 \sqrt{3}=12 \sqrt{3}$

g)
$(-4 \sqrt{12}:(-2 \sqrt{3})=-4*2 \sqrt{3}:-2 \sqrt{3}=-8 \sqrt{3}:-2 \sqrt{3}=4$

h)
$=12*4 \sqrt{2} :4 \sqrt{2}=48 \sqrt{2}:4 \sqrt{2}=12$

Answer 2

a) 4√11 - 7√13 + 3√13 - 5√11 = - √11 - 4√13
b) (2√3 - 5√2 + 3) - (4√3 - 5√2 + 1) = 2√3 - 5√2 + 3 - 4√3 + 5√2 - 1 = 
    - 2√3 + 2
c) (- 3√5) * (- 2√5) = 6 * 5 = 30
d) √150 +√54 = 5√6 + 3√6 = 8√6
e) √10 + √40 = √10 + 2√10 = 3√10
f) 3√48 - 2√108 + 4√300 = 3 * 4√3 - 2 * 2 * 3√3 + 4 * 10√3 = 12√3 - 12√3 + 40√3 = 40√3
g) (- 4√12) : (- 2√3) = (- 4 * 2√3) * (-1/2√3) = 4
h) (12√32) : (4√2) = (12 * 4√2) * (1/4√2) = 12