
(TEST) Understanding Rational and Irrational Numbers
Authored by Stephanie Wofford
Mathematics
9th Grade
CCSS covered
Used 3+ times

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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
2
4
8
16
Answer explanation
The expression \(\sqrt{16}\) asks for the number that, when multiplied by itself, equals 16. The number 4 satisfies this condition, as \(4 \times 4 = 16\). Therefore, the correct answer is 4.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following numbers is irrational?
0.75
2
Answer explanation
The number \( \sqrt{3} \) is irrational because it cannot be expressed as a fraction of two integers. In contrast, \( \frac{1}{2} \), 0.75, and 2 are all rational numbers.
Tags
CCSS.8.NS.A.1
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Answer explanation
To simplify (2^3) \cdot (2^4), use the property of exponents that states a^m \cdot a^n = a^{m+n}. Here, 3 + 4 = 7, so (2^3) \cdot (2^4) = 2^7. Thus, the correct answer is 2^7.
Tags
CCSS.8.EE.A.1
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Rational
Irrational
Answer explanation
The number \(\frac{22}{7}\) is a fraction where both the numerator and denominator are integers. Since it can be expressed as a ratio of two integers, it is classified as a rational number.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Answer explanation
The expression x^{1/3} represents the cube root of x. In radical form, this is written as \sqrt[3]{x}, which is the correct choice. The other options represent different roots or powers.
Tags
CCSS.HSN.RN.A.2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Because both numbers are irrational
Because both numbers are rational
Because the sum of any two numbers is irrational
Answer explanation
The sum of an irrational number, like \sqrt{2}, and a rational number, like 3, is always irrational. Therefore, the correct choice is that \sqrt{2} is irrational and 3 is rational.
Tags
CCSS.HSN.RN.B.3
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Answer explanation
To simplify (x^3y^2)^2, apply the power of a power rule: multiply the exponents. This gives x^(3*2)y^(2*2) = x^6y^4. Thus, the correct answer is x^6y^4.
Tags
CCSS.HSA.APR.A.1
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