What is the value of 55−−√ to the nearest tenth? Show or explain how you got your answer.

9514 1404 393

  √55 ≈ 7.4

Step-by-step explanation:

The easiest way to find the square root of 55 is to use a calculator.

  √55 ≈ 7.4161984871

Rounded to the nearest tenth, this is ...

  √55 ≈ 7.4

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You can make a first approximation of the root by linearly interpolating between the roots of the perfect squares* on either side of 55.

  √49 = 7

  √64 = 8

  √55 ≈ 7 +(55 -49)/(64 -49) = 7 6/15 = 7 2/5

  √55 ≈ 7.4

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* For numbers greater than 3.3, this sort of approximation will give the value of the root accurate to the nearest tenth. The approximation is better for larger numbers.

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step-by-step explanation: