Question

1.sederhanakan bentuk akar di bawah:
a. √108
b.√448
c.√405
d.√432
e.√336

2.hitunglah nilai dari:
a.3√5 + 4√5
b.2√7 - 3√7 - 4√7
c.√32 - √18 + √8
d.√125 - √45 √20
e.10√12 - 2√27 - √75 ​

Answer 1

Ответ:

Пошаговое объяснение:

a. √108 = $\sqrt{36*3}$=$\sqrt{6^{2}*3 }$ =6$\sqrt{3}$

b.√448= $\sqrt{64*7}$= $\sqrt{8^{2}*7 }$=8$\sqrt{7}$

c.√405= $\sqrt{81*5}$=$\sqrt{9^{2}*5 }$ =9$\sqrt{5}$

d.√432=$\sqrt{144*3}$=$\sqrt{12^{2}*3 }$=12$\sqrt{3}$

e.√336=$\sqrt{16*21}$=$\sqrt{4^{2}*21 }$=4$\sqrt{21}$

2.hitunglah nilai dari:

a.3√5 + 4√5 = $\sqrt{5}$(3+4)=7$\sqrt{5}$

b.2√7 - 3√7 - 4√7 = $\sqrt{7}$(2-3-4)=-5$\sqrt{7}$

c.√32 - √18 + √8 = $\sqrt{16*2}$- $\sqrt{9*2}$ + $\sqrt{4*2}$ = $\sqrt{4^{2}*2 }$ - $\sqrt{3^{2} *2}$ + $\sqrt{2^{2}*2 }$

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

d.√125 - √45 - √20 = $\sqrt{25*5}$ - $\sqrt{9*5}$ - $\sqrt{4*5}$ = $\sqrt{5^{2}*5 }$ - $\sqrt{3^{2}*5 }$ - $\sqrt{2^{2}*5 }$ =

= 5$\sqrt{5}$ - 3$\sqrt{5}$ -2 $\sqrt{5}$ = $\sqrt{5}$ (5-3-2) =$\sqrt{5}$ *0=0

e.10√12 - 2√27 - √75 ​= 10$\sqrt{4*3}$ - 2 $\sqrt{9*3}$ - $\sqrt{25*3}$ = 10$\sqrt{2^{2} *3}$ - 2$\sqrt{3^{2}*3 }$ - $\sqrt{5^{2}*3 }$ = 10*2$\sqrt{3}$ - 2*3$\sqrt{3}$ - 5$\sqrt{3}$ = $\sqrt{3}$ (10*2 - 2*3 -5)= $\sqrt{3}$ (20-6-5)=9$\sqrt{3}$