Podcast
Questions and Answers
A square root sign works like a ______.
A square root sign works like a ______.
bracket
The square root of a number multiplied by itself is ______ to the number.
The square root of a number multiplied by itself is ______ to the number.
equal
The ______ root of a number that is then cubed is equal to the number.
The ______ root of a number that is then cubed is equal to the number.
cube
$\sqrt{100 - 36}$ is equal to $\sqrt{64}$ which is equal to ______.
$\sqrt{100 - 36}$ is equal to $\sqrt{64}$ which is equal to ______.
To simplify $\sqrt{16 + 9}$, you first add 16 and 9 to get 25, then find the square root of 25, which is ______.
To simplify $\sqrt{16 + 9}$, you first add 16 and 9 to get 25, then find the square root of 25, which is ______.
$2^5 + 3^3 = 32 + 27 =$ ______.
$2^5 + 3^3 = 32 + 27 =$ ______.
$4^2 + 4^1 = 16 + 4 =$ ______.
$4^2 + 4^1 = 16 + 4 =$ ______.
$10^{-1} - 10^{-2} = 0.1 - 0.01 =$ ______.
$10^{-1} - 10^{-2} = 0.1 - 0.01 =$ ______.
$\sqrt{25} - \sqrt{16} = 5 - 4 =$ ______.
$\sqrt{25} - \sqrt{16} = 5 - 4 =$ ______.
$\sqrt{100} - \sqrt{64} = 10 - 8 =$ ______.
$\sqrt{100} - \sqrt{64} = 10 - 8 =$ ______.
Flashcards
Square Root as Bracket
Square Root as Bracket
A square root sign acts like a bracket, used to simplify expressions under the root.
Square Root Multiplication
Square Root Multiplication
The square root of a number multiplied by itself.
Cube Root Cubed
Cube Root Cubed
A cube root of a number subsequently cubed.
Study Notes
- Calculations with exponents is a topic involving simplifying expressions with square roots and cube roots.
- A square root sign functions like a bracket for order of operations.
- It is possible to simplify any addition or subtraction underneath the square root sign where possible.
- √16 + 9 = √25 = 5 and √169 - 144 = √25 = 5, shows how to simplify.
- The square root of a number multiplied by itself equals the original number, for example (√20)² = 20.
- The cube root of a number that is then cubed is equal to the number, for example (∛20)³ = 20.
Exercise 2.3 - Calculations and Simplifications
- Exercise 2.3 presents multiple problems, requiring simplification of expressions with exponents, square roots, and cube roots.
Simplifying Expressions
- These questions involve using exponent rules and combining terms.
- One must simplify: 2⁵ + 3³, 3⁴ + 3³ + √8, 4² + 4², and 3³ - 3².
- Also requires simplifying: 10⁻¹ - 10.
Finding Values of Expressions with Square Roots
- These questions involve order of operations within square roots.
- This means one must find the values of: √9 + 16, √9 + √16, √25 - 16, √25 - √16, √100 - 64, and √100 - √64.
Simplifying Expressions with Squared Square Roots
- The questions involve the concept of squaring a square root cancels each other out: (√16)², (√64)², (√25)², (√30)², (√48)², and (√120)².
Simplifying Expressions with Cubed Roots
- These questions involve the same concept of cubing a cubed root cancels each other out (∛8)³, (∛27)³, (∛64)³, (∛12)³, (∛1000)³, and (∛250)³.
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