Podcast
Questions and Answers
What is the result of multiplying the surds $2 \times 3$?
What is the result of multiplying the surds $2 \times 3$?
- $4$
- $8$
- $6$ (correct)
- $5$
The square root of $25$ simplifies to $5$.
The square root of $25$ simplifies to $5$.
True (A)
What is the simplified form of $\sqrt{200}$?
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.
$2 + 3\sqrt{5}$ simplifies to _________ when there is another term with $\sqrt{5}$ to add.
Match the following operations with their results:
Match the following operations with their results:
What is the result of the operation $3^2 - 8$?
What is the result of the operation $3^2 - 8$?
What is the result of dividing the surd $12 \div 6$?
What is the result of dividing the surd $12 \div 6$?
What are the results of adding $5 + 3\sqrt{5}$?
What are the results of adding $5 + 3\sqrt{5}$?
$4^3 ÷ 2^6$ equals $24^2$.
$4^3 ÷ 2^6$ equals $24^2$.
What is the simplified form of $15x^3 ÷ 3x^2$?
What is the simplified form of $15x^3 ÷ 3x^2$?
Surds can only be simplified if they contain square numbers.
Surds can only be simplified if they contain square numbers.
The expression $x^{-2}$ can be rewritten in ordinary form as ___.
The expression $x^{-2}$ can be rewritten in ordinary form as ___.
Match the following expressions with their equivalent forms:
Match the following expressions with their equivalent forms:
What is the result of the operation $5 imes 5^2$?
What is the result of the operation $5 imes 5^2$?
The expression $x^2 ÷ x^2$ is equal to 1 for any non-zero x.
The expression $x^2 ÷ x^2$ is equal to 1 for any non-zero x.
What is the result of $32 - 48 - 75$?
What is the result of $32 - 48 - 75$?
What is the ordinary form of $x^{1}$?
What is the ordinary form of $x^{1}$?
The expression $x^{2}$ is equivalent to $x imes x$ in ordinary form.
The expression $x^{2}$ is equivalent to $x imes x$ in ordinary form.
What is the ordinary form of $x^{ rac{1}{2}}$?
What is the ordinary form of $x^{ rac{1}{2}}$?
The expression $x^{1/3}$ represents the __________ of x.
The expression $x^{1/3}$ represents the __________ of x.
Match the ordinary form expressions with their index form expressions:
Match the ordinary form expressions with their index form expressions:
Which of the following is the index form of the expression $x imes x imes x$?
Which of the following is the index form of the expression $x imes x imes x$?
The expression $x^{ rac{1}{4}}$ can be expressed as $x^{4}$ in ordinary form.
The expression $x^{ rac{1}{4}}$ can be expressed as $x^{4}$ in ordinary form.
What is the ordinary form of $x^{2}$?
What is the ordinary form of $x^{2}$?
The index form of $4$ is __________.
The index form of $4$ is __________.
Match the following index forms with their ordinary equivalents:
Match the following index forms with their ordinary equivalents:
Flashcards are hidden until you start studying
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
