Question Video: Finding the Square Root of a Decimal Number | Nagwa Question Video: Finding the Square Root of a Decimal Number | Nagwa

# Question Video: Finding the Square Root of a Decimal Number Mathematics • First Year of Preparatory School

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Calculate −√0.25.

01:58

### Video Transcript

Calculate negative the square root of 0.25.

In this question, we are asked to evaluate the square root of a rational number given as a decimal. We can start by recalling that the square root of 𝑎 is the nonnegative number whose square is 𝑎. We can then recall that it is easier to find the square root of a rational number written as a fraction. So we rewrite 0.25 as one-quarter to obtain negative the square root of one-quarter.

This then gives us two methods of evaluating the square root. Either we can note that one-half squared is one-quarter or we can use the quotient rule for square roots, which tells us that if 𝑎 and 𝑏 are integers with 𝑎 nonnegative and 𝑏 positive, then the square root of 𝑎 over 𝑏 is equal to the square root of 𝑎 over the square root of 𝑏. We can apply this result with 𝑎 equal to one and 𝑏 equal to four to get negative the square root of one over the square root of four.

Finally, we can see that the numerator is the same as the square root of one squared and the denominator is the same as the square root of two squared. Therefore, we can evaluate the roots to obtain negative one-half.

We can check our answer by multiplying one-half by one-half to see that we get one-quarter, which is 0.25. So one-half is the square root of 0.25. Hence, negative the square root of 0.25 is negative one-half.

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