Find $\sqrt{0.4225}$
Find $\sqrt{14.44}$
Find $\sqrt{0.0729}$
Find $\sqrt{7.29}$
Find $\sqrt{0.1089}$
Find $\sqrt{19.36}$
Find $\sqrt{0.2116}$
Find $\sqrt{25.00}$
Find $\sqrt{0.9025}$
Find $\sqrt{31.36}$
Step: Think of this as $\sqrt{\frac{4225}{10000}}$.
Calculation: The square root of $4225$ is $65$ (since $60^2 = 3600$ and $70^2 = 4900$).
Result: $0.65$
Step: Think of this as $\sqrt{\frac{1444}{100}}$.
Calculation: The square root of $1444$ is $38$ (it must end in $2$ or $8$; $30^2 = 900$ and $40^2 = 1600$).
Result: $3.8$
Step: This is $\sqrt{\frac{729}{10000}}$.
Calculation: The square root of $729$ is $27$.
Result: $0.27$
Step: This is similar to the previous problem but with the decimal shifted.
Calculation: $\sqrt{\frac{729}{100}}$.
Result: $2.7$
Step: Look at $1089$. Since $30^2 = 900$ and $40^2 = 1600$, the root is in the $30$s. It ends in $9$, so the root ends in $3$ or $7$.
Calculation: $33 \times 33 = 1089$.
Result: $0.33$
Step: Look at $1936$. $40^2 = 1600$ and $50^2 = 2500$.
Calculation: Since it ends in $6$, we try $44$ or $46$. $44 \times 44 = 1936$.
Result: $4.4$
Step: Look at $2116$. It is slightly less than $2500$ ($50^2$).
Calculation: Trying $46 \times 46 = 2116$.
Result: $0.46$
Step: This is the simplest one in the set.
Calculation: We know $5 \times 5 = 25$.
Result: $5.0$
Step: Any number ending in $25$ has a square root ending in $5$.
Calculation: For $9025$, we look for two consecutive numbers that multiply to $90$ ($9 \times 10$). So the root is $95$.
Result: $0.95$
Step: Look at $3136$. $50^2 = 2500$ and $60^2 = 3600$.
Calculation: It ends in $6$, so we try $54$ or $56$. $56 \times 56 = 3136$.
Result: $5.6$