Calculate the square root of 16.8

Problem

√(,16.8)

Solution

1. Identify the number as a decimal and rewrite it as a fraction to simplify the calculation.

√(,16.8)=√(,168/10)

2. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.

√(,168/10)=√(,84/5)

3. Apply the property of square roots that allows the separation of the numerator and the denominator.

√(,84/5)=√(,84)/√(,5)

4. Factor the numerator to pull out perfect squares. Since 84=4×21 the square root of 4 is 2.

√(,4×21)/√(,5)=(2√(,21))/√(,5)

5. Rationalize the denominator by multiplying both the numerator and the denominator by √(,5)

(2√(,21)×√(,5))/(√(,5)×√(,5))=(2√(,105))/5

6. Calculate the decimal approximation using a calculator or numerical methods.

√(,16.8)≈4.09878

Final Answer

√(,16.8)=(2√(,105))/5≈4.09878

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