Question Video: Finding the Square Root of Mixed Numbers | Nagwa Question Video: Finding the Square Root of Mixed Numbers | Nagwa

Question Video: Finding the Square Root of Mixed Numbers Mathematics • First Year of Preparatory School

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Calculate ±√(3(61/100)).

02:43

Video Transcript

Calculate positive or negative the square root of three and 61 over 100.

In this question, we are asked to calculate the value of an expression. And there are two things that we can start by noting. First, the expression starts with a positive or negative symbol. This means that we will obtain two values: one when we use the positive value and another when we use the negative value. Second, we can see that we are taking the square root of a mixed number. To calculate this root, we first need to rewrite the mixed number as a fraction. And we can do this by rewriting three as 300 over 100. We see that three and 61 over 100 is equal to 361 over 100. Therefore, we can rewrite the expression that we are asked to evaluate as positive or negative the square root of 361 over 100.

We can now see that we want to evaluate the square root of a rational number. And to do this, we can recall the quotient rule for square roots. This tells us that if 𝑎 and 𝑏 are integers with 𝑎 greater than or equal to zero 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 to our expression, with 𝑎 equal to 361 and 𝑏 equal to 100, to obtain positive or negative the square root of 361 over the square root of 100.

We can simplify this expression further by noting that 361 is equal to 19 times 19 and 100 is equal to 10 times 10. So we can rewrite our expression as positive or negative the square root of 19 squared over the square root of 10 squared.

Finally, we can recall that if 𝑐 is nonnegative, then the square root of 𝑐 squared is just equal to 𝑐. We can apply this to each of the square roots to get positive or negative 19 over 10. Hence, we have shown that positive or negative the square root of three and 61 over 100 is equal to either 19 over 10 or negative 19 over 10.

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