How to Simplify Fractions with Radicals

Question

I am returning to school...algebra...trying to use quadratic formula to solve for $x$, have problem seeing how to simplify fractions with radicals. Is there a step by step guide?

I am currently stuck on simplifying the number $\;\sqrt{ \dfrac {253}{441}}.$

Thanks for any help lus any suggestions of how to bone up on simplifying fractions/radicals.

Answer 1

The first step would be to factor the numerator and denominator of the fraction: $$ \sqrt{\frac{253}{441}} = \sqrt{\frac{11 \times 23}{3^2 \times 7^2}} $$ Next, since we can't simplify the fraction by cancelling factors that are common to both the numerator and the denomiantor, we need to consider the radical. To simplify this, we can "pull pairs of factors out of the radical as a single factor:" $$ \sqrt{\frac{11 \times 23}{3^2 \times 7^2}} = \frac{1}{3 \times 7}\sqrt{\frac{11 \times 23}{1}} = \frac{1}{21}\sqrt{\frac{253}{1}} = \frac{\sqrt{253}}{21} $$

Answer 2

Hint $$441 = 21^2$$ $$253 = 11 \cdot 23$$

Also, if you're able to write a question here to ask someone to factorize something for you, you're most likely also capable of using Wolfram|Alpha.

Frankly, I didn't use it, I just noticed that $2 + 3 - 5 = 0$, so $235$ is divisible by $11$, and I know from memory that $441$ is a perfect square. With practice, these things stick to you.

Answer 3

since $441=21^2$ we get for the square root $\frac{\sqrt{253}}{21}$