Square root of a rational quantity: Algebra

Thread starter Miike012
Start date Aug 3, 2011
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Algebra Rational Root Square Square root

In summary, a rational quantity is a number that can be expressed as a ratio of two integers. The square root of a rational quantity is a number that, when multiplied by itself, gives the original rational quantity. To find the square root of a rational quantity, you can use a calculator or a long division method. The square root of a rational quantity can be negative, but in most cases, we refer to the positive square root. There are a few rules for simplifying the square root of a rational quantity, such as taking the square root of perfect squares and cancelling out common factors.

Aug 3, 2011

Miike012

Why arnt the two terms eqaul even though the square root of m was solved properly?

And is this a general rule?

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Aug 3, 2011

Dick

Science Advisor

Homework Helper

I think by 'quadratic surd' they mean that sqrt(m) is irrational where m is rational. Your last expression shows sqrt(m) is a ratio of rationals. Wouldn't that always be rational?

1. What is a rational quantity?

A rational quantity is a number that can be expressed as a ratio of two integers (numbers without decimal points). For example, 3/4 and -2/5 are rational quantities, but 1.5 and √2 are not.

2. What is the square root of a rational quantity?

The square root of a rational quantity is a number that, when multiplied by itself, gives the original rational quantity. For example, the square root of 9 is 3, since 3 x 3 = 9. In other words, the square root of a rational quantity is the number that, when squared, gives the original rational quantity.

3. How do you find the square root of a rational quantity?

To find the square root of a rational quantity, you can use a calculator or a long division method. For example, to find the square root of 9, you can divide 9 by 3 and get 3 as the answer. This method can be used for any rational quantity.

4. Can the square root of a rational quantity be negative?

Yes, the square root of a rational quantity can be negative. For example, the square root of 4 is both 2 and -2, since 2 x 2 = 4 and (-2) x (-2) = 4. However, in most cases, when we refer to the square root of a rational quantity, we mean only the positive square root.

5. Are there any special rules for simplifying the square root of a rational quantity?

Yes, there are a few rules that can help simplify the square root of a rational quantity. For example, if the rational quantity has a perfect square as its numerator or denominator (such as 9/4 or 4/16), you can simplify it by taking the square root of the perfect square. Additionally, if there are any common factors between the numerator and denominator, you can cancel them out to simplify the square root.