# Square and Cube Roots

advertisement
```Square and Cube Roots

Common Core Standard: Use square root and cube root symbols to represent solutions to equations of the
formx2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and
cube roots of small perfect cubes. Know that √2 is irrational.

Common Core Standard: Know that numbers that are not rational are called irrational. Understand informally that
every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually,
and convert a decimal expansion which repeats eventually into a rational number.

Common Core Standard: Use rational approximations of irrational numbers to compare the size of irrational
numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

Rational number- is any number that can be written as a fraction

Irrational number- is any number that cannot be written as a fraction
o
Example: √ = &plusmn;3, which can be written as a fraction or -
o
Example √ = a number that cannot be written as fraction, it is a decimal that does not end or repeat

Square root- is a number that when multiplied by itself gives the number

Cube root- is a number that when multiplied by itself three times gives the number
o
Example √
o
√ = 2, is a cube root
o
Square roots can be either positive or negative, as a two numbers, which have the same sign, when
= &plusmn;4, is a square root
multiplied are always positive
o

Cube roots are always positive
Perfect Squares and Perfect Cubes- a numbers who always have an exact root the two above examples are perfect
square and cube roots

Estimating square roots of non-perfect squares
o
Why – it is important to develop a number sense of non-perfect squares, as these will come up in real world
situations, particularly concerning the Pythagorean Theorem
o
Example: Estimate the square root of 12 to the nearest tenth without a calculator
o
First, determine between which two perfect squares the number is between, in this case 9 and 16, square
root these
o
Now, using the first of the two perfect squares, determine the square of each tenth, until you get as close
as possible to the number

3.12 = 9.61, this is too small, so you can skip to a higher exponent

3.3 =10.89, this is still too small

3.42 = 11.56, this is very close

3.52 = 12.25, this is too big, so we know that the square root of 12 is between 3.4 and 3.5

Which of these is closer? 3.5

So the estimate of the square root of 12 is 3.5
2
```