Radical expressions involving square roots are fundamental in algebra. Simplifying these expressions requires an understanding of the product and quotient properties of radicals, such as the rule that the product of two square roots is the square root of their product. This worksheet covers multiplying radicals with variables, dividing radicals to simplify fractions, and rationalizing denominators by multiplying by conjugates. Students also apply distributive properties and the FOIL method to simplify expressions containing binomial radicals, ensuring that all final answers are in their simplest radical form.
رقم الاختبار834
الصفالصف العاشر المتقدم
المادةرياضيات
الفصلالفصل الثالث
السنة الدراسية2025/2026
عدد الأسئلة14
إجمالي النقاط14
تاريخ الإضافة2026-04-21
الزيارات49
المعلم أو الناشرAmal Salman
اختر إجابة واحدة لكل سؤال. عند الاختيار ستظهر النتيجة فورًا: الأخضر صحيح، والأحمر خطأ، وسيظهر تفسير الإجابة مباشرة إن كان متوفرًا. وبعد آخر سؤال ستظهر الدرجة النهائية تلقائيًا.
Question 1
Points: 1
Multiply and simplify. Assume that all variables are positive. \(\sqrt{8y^5} \cdot \sqrt{40y^2}\)
Explanation
Multiply the radicands: \(\sqrt{8y^5 \cdot 40y^2} = \sqrt{320y^7}\). Simplify by factoring out perfect squares: \(\sqrt{64 \cdot 5 \cdot y^6 \cdot y} = 8y^3\sqrt{5y}\).
Question 2
Points: 1
Divide and simplify. Assume that all variables are positive. \(\frac{\sqrt{600}}{\sqrt{6}}\)
Explanation
Use the quotient property of radicals: \(\sqrt{\frac{600}{6}} = \sqrt{100} = 10\).
Question 3
Points: 1
Divide and simplify. Assume that all variables are positive. \(\frac{\sqrt{180x^5}}{\sqrt{5x^3}}\)
Explanation
Divide the radicands: \(\sqrt{\frac{180x^5}{5x^3}} = \sqrt{36x^2}\). The square root of \(36x^2\) is \(6x\).
Question 4
Points: 1
Simplify \((\sqrt{2} - 3)(\sqrt{2} + 3)\)
Explanation
This is a difference of squares: \((\sqrt{2})^2 - 3^2 = 2 - 9 = -7\).
Question 5
Points: 1
Simplify \((\sqrt{5} - 7)^2\)
Explanation
Use the perfect square binomial formula \((a-b)^2 = a^2 - 2ab + b^2\): \((\sqrt{5})^2 - 2(7)(\sqrt{5}) + 7^2 = 5 - 14\sqrt{5} + 49 = 54 - 14\sqrt{5}\).
Question 6
Points: 1
Rationalize the denominator: \(\frac{1}{2 + \sqrt{3}}\)
Explanation
Multiply the numerator and denominator by the conjugate \(2 - \sqrt{3}\): \(\frac{2 - \sqrt{3}}{(2 + \sqrt{3})(2 - \sqrt{3})} = \frac{2 - \sqrt{3}}{4 - 3} = 2 - \sqrt{3}\).
Simplify the radicals: \(\frac{3(2\sqrt{5})}{3\sqrt{5}} = \frac{6\sqrt{5}}{3\sqrt{5}} = 2\).
Result Tracking
Answered0 / 14
Correct Answers0
Wrong Answers0
Current Percentage0%
Quiz Completed
This is your final result after answering all questions.
Final Result
0/140%
Correct Answers0
Wrong Answers0
Answered Questions0 / 14
Total Possible Points14
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