Question

$\sqrt{} 400 =$
$\sqrt{144 = }$
$\sqrt{225}$
$\sqrt{121 = }$

Answer 1

$\sqrt{400}$

400 | 2
200 | 2
100 | 2
  50 | 2
  25 | 5
   5  | 5
   1

$\sqrt{400}= \sqrt{2\cdot2\cdot2\cdot2\cdot5\cdot5}\\\\\sqrt{400}=\sqrt{2^2\cdot2^2\cdot5^2}\\\\\sqrt{400}=2\cdot2\cdot5\\\\ \sqrt{400}=20$
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$\sqrt{144}$

144 | 2
 72  | 2
 36  | 2
 18  | 2
  9   | 3
  3   | 3
  1

$\sqrt{144}= \sqrt{2\cdot2\cdot2\cdot2\cdot3\cdot3}\\\\ \sqrt{144}= \sqrt{2^2\cdot2^2\cdot3^2}\\\\ \sqrt{144}=2\cdot2\cdot3\\\\ \sqrt{144}=12$
------------------------------------------------------------------

$\sqrt{225}$


225 | 3
  75 | 3
  25 | 5
   5  | 5
   1

$\sqrt{225}= \sqrt{3^2\cdot5^2}\\\\ \sqrt{225}=3\cdot5\\\\ \sqrt{225}=15$
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$\sqrt{121}$

121 | 11
  11 | 11
   1

$\sqrt{121}= \sqrt{11\cdot11} \\\\ \sqrt{121}= \sqrt{11^2}\\\\ \sqrt{121}=11$