Calculate the square root of 37.5

Problem

√(,37.5)

Solution

1. Rewrite the decimal as a fraction to make it easier to simplify.

√(,37.5)=√(,75/2)

2. Rationalize the denominator by multiplying the numerator and denominator by 2 inside the square root.

√(,(75⋅2)/(2⋅2))=√(,150/4)

3. Simplify the square root by pulling out the square root of the denominator and factoring the numerator.

√(,25⋅6)/2

4. Extract the perfect square from the numerator.

(5√(,6))/2

5. Calculate the decimal approximation if needed. Since √(,36)=6 and √(,49)=7 the value is slightly larger than 6.

√(,37.5)≈6.123724

Final Answer

√(,37.5)=(5√(,6))/2

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