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Evaluate the expression: sqrt(1-0,36)+sqrt(2-0,56)+sqrt(3-0,75)=

Evaluate the expression:\newline1−0.36+2−0.56+3−0.75=\sqrt{1-0.36}+\sqrt{2-0.56}+\sqrt{3-0.75}=

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Full solution

Q. Evaluate the expression:\newline1−0.36+2−0.56+3−0.75=\sqrt{1-0.36}+\sqrt{2-0.56}+\sqrt{3-0.75}=
  1. Convert to Fractions: First, let's convert the decimals to fractions to make the square roots easier to handle. 1−0.36+2−0.56+3−0.75=1−36100+2−56100+3−75100\sqrt{1 - 0.36} + \sqrt{2 - 0.56} + \sqrt{3 - 0.75} = \sqrt{1 - \frac{36}{100}} + \sqrt{2 - \frac{56}{100}} + \sqrt{3 - \frac{75}{100}}
  2. Simplify Fractions: Now, simplify the fractions. 1−36100+2−56100+3−75100=1−925+2−1425+3−34\sqrt{1 - \frac{36}{100}} + \sqrt{2 - \frac{56}{100}} + \sqrt{3 - \frac{75}{100}} = \sqrt{1 - \frac{9}{25}} + \sqrt{2 - \frac{14}{25}} + \sqrt{3 - \frac{3}{4}}
  3. Subtract Whole Numbers: Subtract the fractions from the whole numbers. 1−925+2−1425+3−34=2525−925+5025−1425+124−34\sqrt{1 - \frac{9}{25}} + \sqrt{2 - \frac{14}{25}} + \sqrt{3 - \frac{3}{4}} = \sqrt{\frac{25}{25} - \frac{9}{25}} + \sqrt{\frac{50}{25} - \frac{14}{25}} + \sqrt{\frac{12}{4} - \frac{3}{4}}
  4. Simplify Square Roots: Simplify the expressions inside the square roots. 2525−925\sqrt{\frac{25}{25} - \frac{9}{25}} + 5025−1425\sqrt{\frac{50}{25} - \frac{14}{25}} + 124−34\sqrt{\frac{12}{4} - \frac{3}{4}} = 1625\sqrt{\frac{16}{25}} + 3625\sqrt{\frac{36}{25}} + 94\sqrt{\frac{9}{4}}
  5. Take Square Roots: Take the square root of each fraction. 1625+3625+94=45+65+32\sqrt{\frac{16}{25}} + \sqrt{\frac{36}{25}} + \sqrt{\frac{9}{4}} = \frac{4}{5} + \frac{6}{5} + \frac{3}{2}
  6. Add Fractions: Find a common denominator and add the fractions. 45+65+32=(810)+(1210)+(1510)\frac{4}{5} + \frac{6}{5} + \frac{3}{2} = \left(\frac{8}{10}\right) + \left(\frac{12}{10}\right) + \left(\frac{15}{10}\right)

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