To find the square root of these numbers, we can look for perfect squares. A helpful trick is to separate the number into two parts: the digits and the zeros.
1.
Count the zeros: If there is an even number of zeros at the end, take half of them out. For example, $\sqrt{100} = 10$ (two zeros become one zero).
2.
Find the square root of the remaining number: Look at the digits left after removing the zeros. Find what number multiplied by itself equals those digits.
3.
Combine them: Put the result from step 2 together with the zeros from step 1.
Let's solve each one:
*
$\sqrt{12100}$:
* Remove two zeros: $\sqrt{121}$.
* $11 \times 11 = 121$, so $\sqrt{121} = 11$.
* Add back one zero:
110.
*
$\sqrt{28900}$:
* Remove two zeros: $\sqrt{289}$.
* $17 \times 17 = 289$, so $\sqrt{289} = 17$.
* Add back one zero:
170.
*
$\sqrt{40000}$:
* Remove four zeros (half go outside): $\sqrt{4}$.
* $2 \times 2 = 4$, so $\sqrt{4} = 2$.
* Add back two zeros:
200.
*
$\sqrt{36100}$:
* Remove two zeros: $\sqrt{361}$.
* $19 \times 19 = 361$, so $\sqrt{361} = 19$.
* Add back one zero:
190.
*
$\sqrt{22500}$:
* Remove two zeros: $\sqrt{225}$.
* $15 \times 15 = 225$, so $\sqrt{225} = 15$.
* Add back one zero:
150.
*
$\sqrt{8100}$:
* Remove two zeros: $\sqrt{81}$.
* $9 \times 9 = 81$, so $\sqrt{81} = 9$.
* Add back one zero:
90.
*
$\sqrt{10000}$:
* Remove four zeros (half go outside): $\sqrt{1}$.
* $1 \times 1 = 1$, so $\sqrt{1} = 1$.
* Add back two zeros:
100.
*
$\sqrt{16900}$:
* Remove two zeros: $\sqrt{169}$.
* $13 \times 13 = 169$, so $\sqrt{169} = 13$.
* Add back one zero:
130.
*
$\sqrt{6400}$:
* Remove two zeros: $\sqrt{64}$.
* $8 \times 8 = 64$, so $\sqrt{64} = 8$.
* Add back one zero:
80.
*
$\sqrt{32400}$:
* Remove two zeros: $\sqrt{324}$.
* $18 \times 18 = 324$, so $\sqrt{324} = 18$.
* Add back one zero:
180.
*
$\sqrt{19600}$:
* Remove two zeros: $\sqrt{196}$.
* $14 \times 14 = 196$, so $\sqrt{196} = 14$.
* Add back one zero:
140.
*
$\sqrt{25600}$:
* Remove two zeros: $\sqrt{256}$.
* $16 \times 16 = 256$, so $\sqrt{256} = 16$.
* Add back one zero:
160.
Final Answer:
$\sqrt{12100} = 110$
$\sqrt{28900} = 170$
$\sqrt{40000} = 200$
$\sqrt{36100} = 190$
$\sqrt{22500} = 150$
$\sqrt{8100} = 90$
$\sqrt{10000} = 100$
$\sqrt{16900} = 130$
$\sqrt{6400} = 80$
$\sqrt{32400} = 180$
$\sqrt{19600} = 140$
$\sqrt{25600} = 160$
Parent Tip: Review the logic above to help your child master the concept of worksheet on square roots and.
