1/19/17 Week 2 Thursday daily sheet: Roots
Daily aims:




1. I can find perfect square roots of whole numbers and fractions. [ with the calculator by hand ]
2. I can find perfect cube roots of whole numbers and fractions. [ with the calculator by hand ]
3. I grasp the relation between squaring & square rooting and between cubing & finding the cube root.
4. I know the 1st 12 perfect squares and 1st 6 perfect cubes from memory.
Before lesson
1a) Below is a square with an area of 9 square units.
Cut it up to show the 9 little squares inside.
During lesson
1b) What’s the length of 1 side of the big square?
1c) List 3 more areas for squares that would have whole
number side lengths.
2) How might you describe what squaring a number has
to do with physical squares?
3) Finding the square root would be doing what with a
physical square?
D. Stark 1/8/2017
1
4) √49
√
16
81
=
=
5) Below is a cube with a volume of 64 cubic units.
That means you can stack 64 little cubes neatly inside.
What’s the length of 1 of the sides of the big cube?
3
6)
√125 =
3
√−125 =
3
27
√
64
=
6) 60 isn’t a perfect square. √60 doesn’t equal a
whole number. But can you figure out what 2 whole
numbers it’s between?
7) Simplify √20
D. Stark 1/8/2017
2
1/19/17 Week 2 Thursday daily sheet: Roots
Before lesson
1a) Below is a square with an area of 9 square units.
Cut it up to show the 9 little squares inside.
KEY
During lesson
1b) What’s the length of 1 side of the big square?
3 units
1c) List 3 more areas for squares that would have whole
number side lengths. 1, 4, 16 [also 25, 26, … any
perfect square]
2) How might you describe what squaring a number has
to do with physical squares?
Squaring a number is like finding the area of a
square with a side length of that number.
3) Finding the square root would be doing what with a
physical square?
That would be finding the side length of a square if
you’re given its area.
D. Stark 1/8/2017
3
4) √49
√
16
=
81
=
7
𝟒
𝟗
5) Below is a cube with a volume of 64 cubic units.
That means you can stack 64 little cubes neatly inside.
What’s the length of 1 of the sides of the big cube?
𝟑
√𝟔𝟒 = 4 units on 1 side
Cubing a number is essentially finding the volume
of a cube with that side length. Finding the cube
root of a number is basically finding the side length
of a cube with the given number as the volume.
D. Stark 1/8/2017
4
3
3
6) √125 = 5
√−125 = –5
Unlike square roots, cube roots do allow for
negative numbers inside. That’s because there
can be the same number in each blank, resulting in
a negative answer:
________  ________  ________
3
27
√
64
𝟑
=
√𝟐𝟕
𝟑
√𝟔𝟒
=
𝟑
𝟒
7) 60 isn’t a perfect square. √60 doesn’t equal a
whole number. But can you figure out what 2 whole
numbers it’s between?
√𝟒𝟗 = 7
√𝟔𝟎 = ?? somewhere between 7 & 8, closer to 8
√𝟔𝟒 = 8
8) Simplify √20
See if you can find a perfect square factor.
√𝟐𝟎 = √𝟒  𝟓 = √𝟒  √𝟓 = 2  √𝟓 = 2√𝟓
Since there’s no worry about the 2 and the 5 being
mistaken for 25, we don’t bother writing the
multiplication sign in the simplified result, just as
we don’t both writing 3  b but only 3b.
D. Stark 1/8/2017
5