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Questions and Answers
What is the result of multiplying the surds $2 \times 3$?
The square root of $25$ simplifies to $5$.
True
What is the simplified form of $\sqrt{200}$?
10\sqrt{2}
$2 + 3\sqrt{5}$ simplifies to _________ when there is another term with $\sqrt{5}$ to add.
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Match the following operations with their results:
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What is the result of the operation $3^2 - 8$?
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What is the result of dividing the surd $12 \div 6$?
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What are the results of adding $5 + 3\sqrt{5}$?
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$4^3 ÷ 2^6$ equals $24^2$.
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What is the simplified form of $15x^3 ÷ 3x^2$?
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Surds can only be simplified if they contain square numbers.
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The expression $x^{-2}$ can be rewritten in ordinary form as ___.
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Match the following expressions with their equivalent forms:
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What is the result of the operation $5 imes 5^2$?
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The expression $x^2 ÷ x^2$ is equal to 1 for any non-zero x.
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What is the result of $32 - 48 - 75$?
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What is the ordinary form of $x^{1}$?
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The expression $x^{2}$ is equivalent to $x imes x$ in ordinary form.
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What is the ordinary form of $x^{ rac{1}{2}}$?
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The expression $x^{1/3}$ represents the __________ of x.
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Match the ordinary form expressions with their index form expressions:
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Which of the following is the index form of the expression $x imes x imes x$?
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The expression $x^{ rac{1}{4}}$ can be expressed as $x^{4}$ in ordinary form.
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What is the ordinary form of $x^{2}$?
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The index form of $4$ is __________.
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Match the following index forms with their ordinary equivalents:
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Study Notes
Surds
- Multiplying surds: Multiplying surds involves multiplying the values inside the radical symbol. For example, 2√3 × √10 = √60.
- Dividing surds: Dividing surds involves dividing the values inside the radical symbol. For example, √10 ÷ √2 = √5.
- Simplifying surds: Simplifying surds involves taking out perfect square numbers from inside the radical symbol and finding their root. For example, √4a = √(4 × a) = 2√a.
- Adding and subtracting surds: Adding and subtracting surds requires the same surd to be present in both terms. For example, √b + 2√b = 3√b.
Indices
- Multiplying indices: When multiplying indices with the same base, add the exponents. For example, x * x = x².
- Dividing indices: When dividing indices with the same base, subtract the exponents. For example, x ÷ x = x⁻¹.
- Powers of indices: When raising a power to another power, multiply the exponents. For example, (x²)³ = x⁶.
- Negative indices: A negative index represents the reciprocal of the base raised to the positive value of the index. For example, x⁻¹ = 1/x.
- Fractional indices: A fractional index indicates taking the root of the base. For example, x½ = √x.
- Power of zero: Any base raised to the power of zero is equal to one. For example, x⁰ = 1.
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Description
Test your understanding of surds and indices in this algebra quiz. This quiz covers multiplying, dividing, simplifying surds, and the rules for handling indices. Challenge yourself to apply these concepts to various problems.
