What is the square root of 90 simplified in radical form?

What is the square root of 90 simplified in radical form?

 %sqrt(90) = 3sqrt(10)% <h4 class=answerHeader>Explanation:</h4> To simplify <mathjax>%sqrt(90)%</mathjax>, the goal is to find numbers whose product gives the result of <mathjax>%90%</mathjax>, as well as collect pairs of numbers to form our simplified radical form. In our case, we can begin in the following way:<mathjax>%90 -&gt; (30 * 3)%</mathjax><mathjax>%30 -&gt; (10 * 3) %</mathjax> . . . <mathjax>%*%</mathjax>. . . <mathjax>% 3%</mathjax><mathjax>%10 -&gt; (5 * 2) %</mathjax> . . . . . . <mathjax>% *%</mathjax>. . . <mathjax>% underbrace(3*3)_(pair) %</mathjax> Since we dont have numbers we could further divide which yield a number other than <mathjax>%1%</mathjax>, we stop here and collect our numbers. A pair of numbers counts as one number, namely the <mathjax>%3%</mathjax> itself. Thus we can now write <mathjax>%sqrt(90) = 3sqrt(5*2) = 3sqrt(10)%</mathjax>More examples:(1) <mathjax>%sqrt(30)%</mathjax><mathjax>%30 -&gt; (10 * 3)%</mathjax><br></br><mathjax>%10 -&gt; (5 * 2)%</mathjax> . . . <mathjax>% * %</mathjax>. . . <mathjax>%3%</mathjax>We cannot find any more divisible factors, and we certainly dont have a pair of numbers, so we stop here and call it not simplify-able. The one and only answer is <mathjax>%sqrt(30)%</mathjax>. (2) <mathjax>%sqrt(20)%</mathjax><mathjax>%20 -&gt; (10 * 2)%</mathjax><br></br><mathjax>%10 -&gt; (5) * underbrace(2 * 2)_(pair)%</mathjax>Weve found a pair, so we can simplify this one:<mathjax>%sqrt(20) = 2sqrt(5)%</mathjax>(3) <mathjax>%sqrt(56)%</mathjax><mathjax>%56 -&gt; 8 * 7%</mathjax><br></br><mathjax>%8 -&gt; 4 * 2 * 7%</mathjax><br></br><mathjax>%4 -&gt; underbrace(2* 2)_(pair) * 2 * 7%</mathjax>We proceed the same way and write <mathjax>%sqrt(56) = 2sqrt(2*7) = 2sqrt(14)%</mathjax>