Square Roots and Radical Expressions - be careful! Easy to make a mistake…

How to simplify square root and radical expressions.

For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All courses developed and taught by me (experienced and certified math teacher 🤩).
With my courses you CAN reach your math goal! 💪

✓Help with Middle and High School Math (Public/Private Schools)
✓High School & College Math Test Prep
✓Teacher Certification Math Test Prep
✓Homeschool Math Program and Courses for Pre-Algebra, Algebra 1, Geometry, Algebra 2 and Pre-Calculus.

TC Math Notes

[bjorncedervall]

I see another one below who solved it quite directly in the head - I did it according to 8x12 = 96, and 96/3 =32 -> SQRT(32) -> SQRT(2^5) = 4 x SQRT(2). Maximum of 7-8 seconds.

[andrewm]

I’m so used to watching the denominator get rationalized, I didn’t think you’d actually solve the problem this way!

[bobcarn]

I got it right, but simplified it differently along the way. I multiplied the numerators first to get 96, then divided by 3 to get 32, then simplified the 32 into 16*2, making it 4*sqrt(2).

[dhoffman]

Why not start by cancelling sqrt 12 by sqrt 3 = sqrt 4 = 2 ? Then factor out the sqrt 8. Seems simpler and easy to do mentally. Would be more complex if 3 wasn’t a factor of 12.

[mr.mxyzptlks]

Nice step by step solution. I would have extended the root across it all, then do the arithmetic, then apply the root. Turns out, this way one does not even have to rationalize the denominator. It cancels before taking the root🎉

[andrewm]

Quick way. Square root of 8 = 2 x square root of 2. Square root of 12 = 2 times the square root of 3. Whee divided by the square root of 3, the square roots of 3 cancel. So you end up with 2 x the square root of 2 x 2. Multiply the two 2s and you get 4 times the square root of 2. And that’s your answer without needing to rationalize the denominator (because you have factors that cancel each other out, and there is no more radical in the denominator after the cancellations).

[enriqueiii]

I did this in my head, the only part I was not sure if I cross cancel or not 3sq rt and when I saw the answer, I was correct. Thanks John and Happy Thanksgiving to you and family.

[craigpierce]

Really the hard way there! Just square the whole left side, remove roots, work it out (32 without roots) then re-apply the square root. 5.6568

[schwantz]

I went - 8X12= 96 = SR96 / SR3 - then 3 divides into 96, 32 times- so, SR 32 - = SR 2x16, factor out 16 = 4, so answer you understand my breakdown? of the maths not mentally...lol

[timothylacouture]

I had 4 sq root of 2, but I also thought the denominator had to be rationalised

[Nikioko]

Problem which is solved in 30 seconds, put into a 9 minute video...

[rampakeshbharat]

In an earlier video you claimed the sqrt 4 is +/- 2, so why have you not included the negative answer...I don't expect an answer as you don't reply to questions when you're wrong...