To estimate square roots you must know how close the number inside of the square root is to a perfect square.

What is a perfect square?
What is a square root?
Video example

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What is a perfect square?

When we get a perfect square we call the operation squaring. Here is how you get perfect squares:

$\[\mathop 1\nolimits^2 = 1 \times 1 = 1\]$

$\[\mathop 2\nolimits^2 = 2 \times 2 = 4\]$

$\[\mathop 3\nolimits^2 = 3 \times 3 = 9\]$

$\[\mathop 4\nolimits^2 = 4 \times 4 = 16\]$

$\[\mathop 5\nolimits^2 = 5 \times 5 = 25\]$

$\[\mathop 6\nolimits^2 = 6 \times 6 = 36\]$

$\[\mathop 7\nolimits^2 = 7 \times 7 = 49\]$

$\[\mathop 8\nolimits^2 = 8 \times 8 = 64\]$

$\[\mathop 9\nolimits^2 = 9 \times 9 = 81\]$

$\[\mathop 10\nolimits^2 = 10 \times 10 = 100\]$

$\[\mathop 11\nolimits^2 = 11 \times 11 = 121\]$

$\[\mathop 12\nolimits^2 = 12 \times 12 = 144\]$

$\[\mathop 13\nolimits^2 = 13 \times 13 = 169\]$

$\[\mathop 14\nolimits^2 = 14 \times 14 = 196\]$

$\[\mathop 15\nolimits^2 = 15 \times 15 = 225\]$

The first 15 perfect squares are 1,4,9,16,25,36,49,64,81,100,121,144,169,196,225.

Square Roots

Square roots are an opposite operation to squaring . It takes the perfect square and gives as an answer in the form of number that gives that perfect square.

For example:
$\[\sqrt 1 = 1 \]$
because 1 times 1 is 1
$\[\sqrt 4 = 2 \]$
because 2 times 2 is 4
$\[\sqrt 9 = 3 \]$
because 3 times 3 is 9
$\[\sqrt 16 = 4 \]$
$\[\sqrt 25 = 5 \]$
$\[\sqrt 36 = 6 \]$
$\[\sqrt 49 = 7 \]$
$\[\sqrt 64 = 8 \]$
$\[\sqrt 81 = 9 \]$
$\[\sqrt 100 = 10 \]$
$\[\sqrt 121 = 11 \]$
$\[\sqrt 144 = 12 \]$
$\[\sqrt 169 = 13 \]$
$\[\sqrt 196 = 14 \]$
$\[\sqrt 225 = 15 \]$

To estimate a square root try to see how close your perfect square is to the number under the square root.

For example in
$\[\sqrt 17 \]$
17 is between the perfect squares 16 and 25. It is really close to 16 so since

$\sqrt16=4$
and
$\sqrt 25=5$
then estimates to
$\[\sqrt 1 7 \approx 4.1\]$









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Estimating square roots game

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