Squares, Cubes, and Special Powers Review

Flashcards covering squares, cubes, special powers, square root approximations, fraction-to-decimal conversions, and arithmetic shortcuts based on the lecture notes.

, the value of $13^2$ is __________.

$$169$$

the value of $14^2$ is __________.

$$196$$

the value of $15^2$ is __________.

$$225$$

the value of $25^2$ is __________.

$$625$$

the value of $6^3$ is __________.

$$216$$

the value of $2^6$ is __________.

$$64$$

the value of $3^5$ is __________.

$$243$$

the value of $4^4$ is __________.

$$256$$

the value of $5^4$ is __________.

$$625$$

In geometry, the side ratios of a Right Isosceles ($45-45-90$) triangle are represented as $x : x :$ __________.

xv2

In geometry, the side ratios of a $30-60-90$ triangle are represented as __________.

$$2x$$

The approximate value of sqrt{2}} in the Roots Approximation List is __________.

$$1.4$$

The approximate value of \text{\sqrt{3}} in the Roots Approximation List is __________.

$$1.7$$

The approximate value of \text{\sqrt{7}} in the Roots Approximation List is __________.

$$2.6$$

The approximate value of \text{\sqrt{10}} in the Roots Approximation List is __________.

$$3.2$$

For values larger than \text{\sqrt{4}}, the Memory Rule for square roots suggests adding approximately __________ per digit.

$$0.2$$

For values smaller than \text{\sqrt{4}}, the Memory Rule for square roots suggests subtracting approximately __________.

$$0.3$$

In the sample problem analysis, the approximate sum of \text{\sqrt{2}} + \text{\sqrt{6}} + \text{\sqrt{8}} is calculated as __________.

$$6.6$$

The decimal equivalent of the fraction $\frac{1}{6}$ is approximately __________.

$$0.16$$

The decimal equivalent of the fraction $\frac{1}{8}$ is __________.

$$0.125$$

The decimal equivalent of the fraction $\frac{1}{12}$ is approximately __________.

$$0.08$$

If $\frac{1}{11} = 0.0909...$, then the derived decimal value for $\frac{3}{11}$ is __________.

$$0.2727...$$

In the decimal equivalent of $\frac{3}{11}$, the $16th$ digit after the decimal is __________ because all even-placed digits follow this pattern.

$$7$$

The arithmetic shortcut known as __________ involves breaking numbers into manageable parts that are multiples of the divisor, such as calculating $168 \div 14$ as $(140 + 28) \div 14$.

Chunking

Using the Multiplication Trick, $12 \times 12.5$ is solved as $12(12 + 0.5) = 144 + 6 =$ __________.

$$150$$