Subcategories

• Day 5

  Sum Patterns

  Module 4 Day 5 Challenge Part 1 Module 4 Day 5 Challenge Part 2 Module 4 Day 5 Challenge Part 3 Module 4 Day 5 Challenge Part 4 Module 4 Day 5 Your Turn Part 1 Module 4 Day 5 Your Turn Part 2 Module 4 Day 5 Your Turn Part 3 Module 4 Day 5 Your Turn Part 4
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  A

  @the-blade-dancer So sorry for the late response! Basically, the sentence explains why we think that 162 * r^8 = 32/81. It's essentially an educated guess...

  As the solution says, the denominator of 32/81 is 3^4. This is the same thing as saying the number has a factor of 3^-4 (because 32/81 = 32 * 1/81 = 32 * (1/3^4) = 32 * 3^-4). On the other hand, 162 has a factor of 3^4 = 81. So to get from 162 to 32/81, thinking purely in terms of the powers of 3, we are trying to get from

  3^4 * something to 3^(-4) * something

  Well, to do that, we have to divide by 3^8. We just found that the ratio is sqrt(2)/3, so we want to multiply by the ratio 8 times: this gives (sqrt(2))^8 / 3^8 so it's like dividing by 3^8, which is what we want.

  I hope that makes sense!

• Day 6

  Squares and Roots

  Module 4 Day 6 Challenge Part 1 Module 4 Day 6 Challenge Part 2 Module 4 Day 6 Challenge Part 3 Module 4 Day 6 Your Turn Part 1 Module 4 Day 6 Your Turn Part 2
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  Q

  Great question, @the-blade-dancer !

  If you remember the binomial theorem at all from Module 3 (let me know if you need more explanation here), but we can use a shortcut for the expansion of \((\sqrt{a}+\sqrt{b})^3\).

  In general, \((x+y)^3=x^3+3x^2y+3xy^2+y^3\), so

  \((\sqrt{a}+\sqrt{b})^3=a\sqrt a +3a\sqrt b+ 3\sqrt a b+b\sqrt b\)
  \((\sqrt{a}+\sqrt{b})^3= (a+3b)\sqrt a+(3a+b)\sqrt b\)

  This gets us straight to the form that we need. And since this has to be equal to \(22\sqrt 7+26\sqrt 5\), it is most likely that \(a=7, b=5\), so we can go and check that out. After confirming that it is true, we get that our answer is \(7+5=\boxed{12}\). Let me know if you have any other questions!

• Day 7

  Fractional Powers

  Module 4 Day 7 Challenge Part 1 Module 4 Day 7 Challenge Part 2 Module 4 Day 7 Challenge Part 3 Module 4 Day 7 Your Turn Part 1 Module 4 Day 7 Your Turn Part 2 Module 4 Day 7 Your Turn Part 3
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  B

  I would want to ask a question , 3 √(2) × 6 √(2) I calculated it is bigger than √(3) ÷ 6 √(3)

  3 √(2) × 6 √(2)=36. 36>0.5
  √(3) ÷ 6 √(3)=0.5

• Day 8

  Decimals to Fractions

  Module 4 Day 8 Challenge Part 1 Module 4 Day 8 Challenge Part 2 Module 4 Day 8 Challenge Part 3 Module 4 Day 8 Your Turn Part 1
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  Q

  @dashingrhinoceros Awesome! 😄