جد قيمة الجذر التربيعي والجذر التكعيبي لكل مما يأتي:

$\sqrt{144}$

$\begin{array}{r}\sqrt{144}=\sqrt{2^4\times 3^2}\\ =2^2\times 3=12\end{array}$

الاختبار القبلي

استعمل ترتيب العمليات لتحسب ذهنياً:

$\begin{array}{rl}& 14+15\end{array}$

$10+15=15+14=29$

$\begin{array}{rl}& 6\times 12\end{array}$

$16\times 12=12\times 6=72$

$\begin{array}{rl}& (25+35)÷9\end{array}$

$(25+35)÷9=60÷9=6.666$

$\begin{array}{rl}& 8^2\end{array}$

$8^2=8\times 8=64$

$\begin{array}{rl}& (10{)}^2\end{array}$

${10}^2=10\times 10=100$

$(15{)}^2$

${15}^2=15\times 15=225$

استعمل ترتيب العمليات وجد الناتج لكل مما يأتي:

$\begin{array}{rl}& (6-7)\times (10+4{)}^2-20\end{array}$

$\begin{array}{rl}& (-1)\times (14{)}^2-20\\ & =-1\times 196-20\\ & =-196-20=-216\end{array}$

$\begin{array}{rl}& 100÷4+2\times (-2)\end{array}$

$\begin{array}{rl}& 25+(-4)\\ & =25+(-4)=21\end{array}$

$\begin{array}{rl}& 50÷5+4\times (-4)\end{array}$

$10+(-16)=-(16-10)=-6$

$\begin{array}{rl}& 5-6\times {10}^2+4-2\times (-4)\end{array}$

$\begin{array}{rl}& 5-6\times 100+4-(-8)\\ & =5-600+4+8\\ & =(5+8+4-600)\\ & =17-600=-583\end{array}$

$\begin{array}{rl}& (56÷7{)}^2+(60÷3)\end{array}$

$8^2+20=64+20=84$

$\begin{array}{rl}& (6\times 20)+2(-4)÷6\end{array}$

$\begin{array}{rl}& 120+(-12÷6)\\ & =120+(-2)=118\end{array}$

جد قيمة العبارات الجبرية الآتية:

$\begin{array}{lll}4X-6^2& ,& X=3\end{array}$

$\begin{array}{rl}& 4X-6^2=4\times 3-6^2\\ & =12-36=-24\end{array}$

$\begin{array}{lll}2\mathrm{X}+8& ,& \mathrm{X}=4\end{array}$

$\begin{array}{rl}2X+8& =2\left(4\right)+8\\ & =8+8=16\end{array}$

$\begin{array}{lll}7(x-3)& ,& X=-1\end{array}$

$\begin{array}{rl}& 7(X-3)=7(-1-3)\\ & =7\times (-4)=-28\end{array}$

$\begin{array}{lll}\sqrt{36}\mathrm{y}-4& ,& \mathrm{y}=2\end{array}$

$\begin{array}{rl}& \sqrt{36}y-4=\sqrt{36}\times 2-4\\ & =6\times 2-4=12-4=8\end{array}$

$\begin{array}{lll}|-9|+y^2-25& ,& y=-5\end{array}$

$\begin{array}{rl}& |-9|+y^2-25\\ & =|-9|+(-5{)}^2-25\\ & =9+\left(25\right)-25=9\end{array}$

$\begin{array}{lll}3Z+4& ,& \mathrm{Z}=-1\end{array}$

$\begin{array}{rl}& 3Z+4=3(-1)+4\\ & =-3+4=1\end{array}$

حل معادلات الجمع والطرح لكل مما يأتي:

$\begin{array}{rl}& X-9=8\end{array}$

$x=8+19\Rightarrow x=27$

$\begin{array}{rl}& Z-4=8\end{array}$

$z=8+4\Rightarrow z=12$

$\begin{array}{rl}& h+3=12\end{array}$

$H=12-3\Rightarrow H=9$

$\begin{array}{rl}& 27-Z=24\end{array}$

$\begin{array}{rl}& 27-24=z\\ & z=27-24\Rightarrow z=3\end{array}$

$\begin{array}{rl}& y+3=9\end{array}$

$y=9-3\Rightarrow y=6$

$\begin{array}{rl}& v-5=10\end{array}$

$v=10-5\Rightarrow v=15$

$\begin{array}{rl}& y+11=11\end{array}$

$y=11-11\Rightarrow y=0$

$\begin{array}{rl}& X+|-10|=5\end{array}$

$\begin{array}{r}x+10=5\Rightarrow x=5-10\\ x=-5\end{array}$

$\begin{array}{rl}& \sqrt{16}+y=4\end{array}$

$4+y=4\Rightarrow y=4-4\Rightarrow y=0$

حل معادلات الضرب والقسمة لكل مما يأتي:

$\begin{array}{rl}& x÷8=2\end{array}$

$x=2\times 8\Rightarrow x=16$

$\begin{array}{rl}& Z÷6=3\end{array}$

$z=3\times 6\Rightarrow z=18$

$\begin{array}{rl}& r÷\sqrt{49}=7\end{array}$

$R÷7=7\Rightarrow R=7\times 7\Rightarrow R=49$

$\begin{array}{rl}& 48÷y=\frac{1}{6}\end{array}$

$\begin{array}{rl}& 48=\frac{1}{6}\times y\Rightarrow 48=\frac{y}{6}\\ & y=6\times 48\Rightarrow y=288\end{array}$

$\begin{array}{rl}& X\times \frac{1}{2}=2\end{array}$

$x÷\frac{1}{2}\Rightarrow x=2\times \frac{2}{1}\Rightarrow x=4$

$\begin{array}{rl}& X\times \frac{1}{12}=6\end{array}$

$x=6÷\frac{1}{12}\Rightarrow x=6\times \frac{12}{1}\Rightarrow x=72$

$\begin{array}{rl}& 71\times y=213\end{array}$

$y=213÷71\Rightarrow y=3$

$\begin{array}{rl}& 8\times y=64\end{array}$

$y=64÷8\Rightarrow y=8$

$\begin{array}{rl}& 7\times k=42\end{array}$

$K=42÷7\Rightarrow K=6$

جد قيمة الجذر التربيعي والجذر التكعيبي لكل مما يأتي:

$\sqrt{64}$

$\begin{array}{rl}& \sqrt{64}=\sqrt{2^6}=2^3=8\end{array}$

$\sqrt{100}$

$\sqrt{100}=\sqrt{{10}^2}=10$

$\sqrt{81}$

$\begin{array}{rl}& \sqrt{81}=\sqrt{3^4}=3^2=9\end{array}$

$\sqrt{144}$

$\begin{array}{r}\sqrt{144}=\sqrt{2^4\times 3^2}\\ =2^2\times 3=12\end{array}$

$\sqrt{900}$

$\begin{array}{r}\sqrt{900}=\sqrt{3^2\times 2^2\times 5^2}\\ =3\times 2\times 5=30\end{array}$

$\sqrt{625}$

$\begin{array}{rl}& \sqrt{625}=\sqrt{5^4}=5^2=25\end{array}$

$\sqrt[3]{-125}$

$\begin{array}{rl}& \sqrt[3]{-125}=-\sqrt[3]{125}=-\sqrt[3]{5^3}=-5\end{array}$

$\sqrt[3]{216}$

$\begin{array}{rl}& \sqrt[3]{216}=\sqrt[3]{2^3\times 3^3}=2\times 3=6\end{array}$