ចំនួនអសនិទាន -Hw-01

លំហាត់រ៉ាឌីកាល់ ថ្នាក់ទី ៩

ប្រធានលំហាត់

ចូរគណនា និងសម្រួលកន្សោមរ៉ាឌីកាល់ខាងក្រោម៖

1. $A=\sqrt{12}$

2. $B=3\sqrt{50}$

3. $C=2\sqrt{5}+4\sqrt{5}$

4. $D=7\sqrt{2}-3\sqrt{2}$

5. $E=\sqrt{8}+\sqrt{18}$

6. $F=\sqrt{27}-\sqrt{12}$

7. $G=2\sqrt{20}-\sqrt{45}+3\sqrt{5}$

8. $H=\sqrt{75}+2\sqrt{48}-\sqrt{108}$

9. $I=\sqrt{32}-2\sqrt{50}+\sqrt{98}$

10. $J=\sqrt{24}-\sqrt{54}+\sqrt{150}$

11. $K=\frac{1}{2}\sqrt{72}+\frac{1}{3}\sqrt{162}$

12. $L=5\sqrt{12}-2\sqrt{27}+\sqrt{48}-3\sqrt{75}$

13. $M=2\sqrt{8}+3\sqrt{27}-\sqrt{18}-2\sqrt{12}$

ចម្លើយ និងដំណោះស្រាយសង្ខេប

ខាងក្រោមនេះជាចម្លើយ និងរបៀបបំបែករ៉ាឌីកង់ជាផលគុណកត្តា ដើម្បីងាយស្រួលក្នុងការផ្ទៀងផ្ទាត់៖

1. $A=\sqrt{4\times3}=2\sqrt{3}$

2. $B=3\sqrt{25\times2}=3\times5\sqrt{2}=15\sqrt{2}$

3. $C=(2+4)\sqrt{5}=6\sqrt{5}$

4. $D=(7-3)\sqrt{2}=4\sqrt{2}$

5. $E=\sqrt{4\times2}+\sqrt{9\times2}$
$=2\sqrt{2}+3\sqrt{2}=5\sqrt{2}$

6. $F=\sqrt{9\times3}-\sqrt{4\times3}$
$=3\sqrt{3}-2\sqrt{3}=\sqrt{3}$

7. $G=2\sqrt{4\times5}-\sqrt{9\times5}+3\sqrt{5}$
$=2(2\sqrt{5})-3\sqrt{5}+3\sqrt{5}$
$=4\sqrt{5}-3\sqrt{5}+3\sqrt{5}=4\sqrt{5}$

8. $H=\sqrt{25\times3}+2\sqrt{16\times3}-\sqrt{36\times3}$
$=5\sqrt{3}+2(4\sqrt{3})-6\sqrt{3}$
$=5\sqrt{3}+8\sqrt{3}-6\sqrt{3}=7\sqrt{3}$

9. $I=\sqrt{16\times2}-2\sqrt{25\times2}+\sqrt{49\times2}$
$=4\sqrt{2}-2(5\sqrt{2})+7\sqrt{2}$
$=4\sqrt{2}-10\sqrt{2}+7\sqrt{2}=\sqrt{2}$

10. $J=\sqrt{4\times6}-\sqrt{9\times6}+\sqrt{25\times6}$
$=2\sqrt{6}-3\sqrt{6}+5\sqrt{6}=4\sqrt{6}$

11. $K=\frac{1}{2}\sqrt{36\times2}+\frac{1}{3}\sqrt{81\times2}$
$=\frac{1}{2}(6\sqrt{2})+\frac{1}{3}(9\sqrt{2})$
$=3\sqrt{2}+3\sqrt{2}=6\sqrt{2}$

12. $L=5(2\sqrt{3})-2(3\sqrt{3})+4\sqrt{3}-3(5\sqrt{3})$
$=10\sqrt{3}-6\sqrt{3}+4\sqrt{3}-15\sqrt{3}=-7\sqrt{3}$

13. $M=2(2\sqrt{2})+3(3\sqrt{3})-3\sqrt{2}-2(2\sqrt{3})$
$=4\sqrt{2}+9\sqrt{3}-3\sqrt{2}-4\sqrt{3}$
(ផ្តុំតួដែលមានរ៉ាឌីកង់ដូចគ្នា)
$=(4\sqrt{2}-3\sqrt{2})+(9\sqrt{3}-4\sqrt{3})=\sqrt{2}+5\sqrt{3}$

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