Question

please answer step by step​

Answer 1

Answer:

Step-by-step explanation:

$\sqrt{(144)10^2 + (10 - \frac{1}{100})^2 } \\\\= \sqrt{{(12^2)10^2 + (\frac{999}{100} )^2} }\\\\= \sqrt{\frac{[(120^2)100^2 + 999^2]}{100^2} } \\\\= \frac{1}{100} \sqrt{1000^2(144) + (1000 - 1)^2} \\\\= \frac{1}{100} \sqrt{1000^2(144) + 1000^2 - 2000 + 1}\\\\= \frac{1}{100} \sqrt{1000^2(144 + 1) - 1999}\\\\= \frac{1}{100} \sqrt{145000000 - 1999}\\\\= \frac{1}{100} \sqrt{144998001}\\\\= \frac{1}{100} (12041.5)\\\\= 12.0415\\\\= 12$