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Questions and Answers
What is the value of $\sqrt{25+16}$?
What is the value of $\sqrt{25+16}$?
5
If $x^2 = a$, then $x = \pm \sqrt{a}$. If $x$, then $x =$?
If $x^2 = a$, then $x = \pm \sqrt{a}$. If $x$, then $x =$?
2y
Which operation simplifies radicals correctly?
Which operation simplifies radicals correctly?
- $\sqrt{a} \div \sqrt{b} = \sqrt{\frac{a}{b}}$
- $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$ (correct)
- $\sqrt{a} + \sqrt{b} = \sqrt{a + b}$
- $(\sqrt{a})^n = \sqrt{a^n} = a^n$
What is the value of $\sqrt{38+84}$?
What is the value of $\sqrt{38+84}$?
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What is the value of √25 + 16?
What is the value of √25 + 16?
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If 𝑥 = 2𝑦, then 𝑥 = ______?
If 𝑥 = 2𝑦, then 𝑥 = ______?
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Complete the pattern
Complete the pattern
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Match the following:
Match the following:
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Study Notes
Important Roots
- The symbol √ is used to denote the square root of a number.
- The symbol √ can be used to simplify expressions involving square roots.
Basic Rules
- The rule √a × √b = √(a × b) is used to simplify expressions involving square roots.
- The rule (√a)^n = √(a^n) is used to simplify expressions involving square roots and exponents.
Simplifying Radicals
- Simplifying radicals involves combining like terms and simplifying expressions involving square roots.
- Examples of simplifying radicals include:
- √8 = √(4 × 2) = √4 × √2 = 2√2
- √20 = √(4 × 5) = √4 × √5 = 2√5
- √9 = √(3 × 3) = √3 × √3 = 3
Properties of Square Roots
- If x^2 = a, then x = ±√a
- Examples of using this property include:
- If x^2 = 9, then x = ±√9 = ±3
- If x^2 = 16, then x = ±√16 = ±4
Comparing Square Roots
- Comparing square roots involves determining whether one square root is greater than, less than, or equal to another.
- Examples of comparing square roots include:
- Comparing √101 and √100: √101 > √100
- Comparing √0.81 and √0.9: √0.81 < √0.9
Important Roots
- The symbol √ is used to denote the square root of a number.
- The symbol √ can be used to simplify expressions involving square roots.
Basic Rules
- The rule √a × √b = √(a × b) is used to simplify expressions involving square roots.
- The rule (√a)^n = √(a^n) is used to simplify expressions involving square roots and exponents.
Simplifying Radicals
- Simplifying radicals involves combining like terms and simplifying expressions involving square roots.
- Examples of simplifying radicals include:
- √8 = √(4 × 2) = √4 × √2 = 2√2
- √20 = √(4 × 5) = √4 × √5 = 2√5
- √9 = √(3 × 3) = √3 × √3 = 3
Properties of Square Roots
- If x^2 = a, then x = ±√a
- Examples of using this property include:
- If x^2 = 9, then x = ±√9 = ±3
- If x^2 = 16, then x = ±√16 = ±4
Comparing Square Roots
- Comparing square roots involves determining whether one square root is greater than, less than, or equal to another.
- Examples of comparing square roots include:
- Comparing √101 and √100: √101 > √100
- Comparing √0.81 and √0.9: √0.81 < √0.9
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Description
Test your understanding of roots and radicals, including basic rules and simplification techniques. Practice solving problems involving square roots and cube roots.
