Calculate the square root of 67.5

Problem

√(,67.5)

Solution

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

√(,67.5)=√(,135/2)

2. Multiply the numerator and denominator by 2 to create a perfect square in the denominator.

√(,(135⋅2)/(2⋅2))=√(,270/4)

3. Factor the numerator to find the largest perfect square.

√(,(9⋅30)/4)

4. Simplify the square root by taking the square root of the perfect squares 9 and 4.

(3√(,30))/2

5. Calculate the approximate decimal value using the fact that 8=64 and 9=81

√(,67.5)≈8.2158

Final Answer

√(,67.5)=(3√(,30))/2≈8.2158

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