موقع المناهج
>>
المناهج الإماراتية
المناهج السعودية
المناهج الكويتية
المناهج القطرية
المناهج العمانية
المناهج البحرينية
المناهج السورية
>>
اختر صفًا
الصف الأول
الصف الثاني
الصف الثالث
الصف الرابع
الصف الخامس
الصف السادس
الصف السابع
الصف الثامن
الصف التاسع العام
الصف العاشر العام
الصف الحادي عشر العام
الصف الثاني عشر العام
الصف العاشر المتقدم
الصف الحادي عشر المتقدم
الصف الثاني عشر المتقدم
الصف التاسع المتقدم
الصف العاشر
الصف الحادي عشر
الصف الثاني عشر
الصف التاسع
KG1
KG2
مرحلة ابتدائية
مرحلة متوسطة
مرحلة ثانوية
ملفات جامعية
أخبار
ملفات مدرسية
اختبار اختيار من متعدد تفاعلي: revision on nth roots and rational exponent - Reveal
This worksheet provides a comprehensive review of nth roots and rational exponents. It covers converting between radical and exponential forms, simplifying complex algebraic expressions with fractional exponents, and solving radical equations by isolating the radical. Key concepts include identifying real roots for various indices and applying exponent laws to simplify products and quotients of terms with rational powers.
🏆 انضم إلى التحدي واحصل على ترتيبك
اختبار شهادة تدريبي مؤقت للصف والمادة والفصل نفسه.
ابدأ السباق ✨
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.
Rewrite into rational exponent form: \( \sqrt{10} \)
Explanation
A square root can be written as a rational exponent with an index of 2, so \( \sqrt{10} = 10^{1/2} \).
Simplify:
323/5
Explanation
323/5 = (321/5 )3 = 23 = 8 .
Simplify: \( (\sqrt{16})^3 \)
Explanation
\( (\sqrt{16})^3 = 4^3 = 64 \).
Write as a radical expression: y2/3
A
2y3
B
\( \sqrt{y^3} \)
C
\( \sqrt[3]{y^2} \)
D
3y2
Explanation
Using the rule \( y^{m/n} = \sqrt[n]{y^m} \), the expression y2/3 becomes \( \sqrt[3]{y^2} \).
Simplify the following expression:
85/3
Explanation
85/3 = (81/3 )5 = 25 = 32 .
Simplify:
64-2/3
Explanation
\( 64^{-2/3} = \frac{1}{64^{2/3}} = \frac{1}{(\sqrt[3]{64})^2} = \frac{1}{4^2} = \frac{1}{16} \).
Solve the equation: \( \sqrt{q+1} = 2 \)
Explanation
Squaring both sides gives q+1 = 4 , so q = 3 .
What is the first step to solve: \( p = \sqrt{4p+8} - 3 \)?
A
square both sides
B
subtract 8 on both sides
C
add 3 on both sides
D
divide by 4 on both sides
Explanation
To solve a radical equation, you must first isolate the radical. Adding 3 to both sides results in \( p+3 = \sqrt{4p+8} \).
What is the first step to solve:
(41k-31)1/4 = 5 ?
A
divide by 41 on both sides
B
add 31 on both sides
C
multiply both sides by 4
D
raise both sides to the 4th power
Explanation
The expression is already isolated. To eliminate the exponent of 1/4 , raise both sides to the power of 4.
Solve for x: 6x5 = -192
Explanation
x5 = -192/6 = -32 . The fifth root of -32 is -2.
Simplify. Your answer should contain only positive exponents:
yx1/3 × xy3/2
A
x4/3 y5/2
B
x2/3 y1/2
C
x1/3 y3/2
D
x2/3 y4/3
Explanation
Multiply the variables by adding their exponents: x1/3+1 = x4/3 and y1+3/2 = y5/2 .
Simplify. Your answer should contain only positive exponents: \( \frac{a^2 b^0}{3a^4} \)
A
1
B
\( \frac{1}{3a^2} \)
C
\( \frac{a^2}{3a^4} \)
D
\( \frac{1}{3a^4} \)
Explanation
Since b0 = 1 , the expression is \( \frac{a^2}{3a^4} \). Subtracting exponents gives \( \frac{1}{3a^{4-2}} = \frac{1}{3a^2} \).
Simplify. Your answer should contain only positive exponents:
(x0 y1/3 )3/2 × x0
Explanation
Since x0 = 1 , the expression simplifies to (y1/3 )3/2 . Multiply exponents: 1/3 × 3/2 = 1/2 .
Find the indicated real nth root(s) of a: n = 6, a = -729
A
3
B
-3
C
\( \pm 3 \)
D
no real roots
Explanation
An even root (n=6) of a negative number has no real solution.
Find the indicated real nth root(s) of a: n = 4, a = 256
A
-4
B
4
C
\( \pm 4 \)
D
no real roots
Explanation
For an even index (n=4) and a positive radicand, there are two real roots: positive and negative. Since 44 = 256 , the roots are \( \pm 4 \).
Match the equivalent expression: \( 1/(\sqrt[4]{5}) \)
A
54/3
B
-51/4
C
53/4
D
5-1/4
Explanation
The fourth root is 51/4 . Because it is in the denominator, the exponent becomes negative: 5-1/4 .
Match the equivalent expression: \( (\sqrt[4]{5})^3 \)
A
54/3
B
-51/4
C
53/4
D
5-1/4
Explanation
\( \sqrt[4]{5} \) is 51/4 . Raising this to the 3rd power gives (51/4 )3 = 53/4 .
Result Tracking
Answered
0 / 17
Correct Answers
0
Wrong Answers
0
Current Percentage
0%
Quiz Completed
This is your final result after answering all questions.
Final Result
0/17
0%
Correct Answers
0
Wrong Answers
0
Answered Questions
0 / 17
Total Possible Points
17
You can reopen the page to start again.
