Maths

• In the expression $2^3$, what is the base?


  2
• What is a perfect square?

  A number that has a whole number as its square root
• What is an example of an irrational square root?

  $\sqrt{2}$
• How can you estimate $\sqrt{50}$?


  Estimate between $\sqrt{49} =$$7$ and $\sqrt{64} =$$8$
• What is the result of $2^3 \times 2^4$?


  $2^7$
• What is the result of $(3^2)^3$?


  $3^6$
• What is the result of $2^5 \div 2^2$?


  $2^3$
• Which symbol is associated with surds?

  Square root symbol $\sqrt{x}$
• How can $\sqrt{12}$ be simplified?


  $2\sqrt{3}$
• What is the simplified form of $\sqrt{50}$?


  $5\sqrt{2}$
• What are the steps to simplify a surd?

  1. Find the largest perfect square factor
  2. Take the square root of that factor
  3. Multiply by the remaining simplified root
• What is the simplified form of $\sqrt{72}$?


  $6\sqrt{2}$
• What is the simplified form of $\sqrt{108}$?


  $6\sqrt{3}$
• What is the result of multiplying $3\sqrt{2} \times 4\sqrt{5}$?


  $12\sqrt{10}$
• What is the process for dividing surds?

  • Divide coefficients
  • Divide numbers under the roots
• What is the process for multiplying surds?

  • Multiply coefficients
  • Multiply numbers under the roots
• How do you add and subtract surds?

  • Combine like terms (same root)
• What is the simplified form of $5\sqrt{7} +$$2\sqrt{7}$?


  $7\sqrt{7}$
• What does rationalizing the denominator mean?

  • Eliminating surds from the denominator
• What is the first step to rationalize $\frac{4}{\sqrt{3} - 2}$?


  Multiply by the conjugate $\sqrt{3} +$$2$
• What is the rationalized form of $\frac{4}{\sqrt{3} - 2}$?


  $-4\sqrt{3} - 8$
• What is the result of rationalizing $\frac{1}{\sqrt{2}}$?


  $\frac{\sqrt{2}}{2}$
• What does rationalizing denominators mean?

  Getting rid of square roots in a fraction's denominator
• What are the steps to rationalize a denominator with addition/subtraction?


  1. Identify the conjugate of the denominator
  2. Multiply the numerator and denominator by the conjugate
  3. Simplify the resulting expression
• What is the goal of rationalizing the denominator?


  Make the bottom a normal number
• What is the conjugate of $\sqrt{7} - 3$?


  $\sqrt{7} +$$3$