SAT Algebra – Square Roots

Square roots are a nasty beast for many students trying to rock the SAT. Trust me, I know. The problem is very similar to the problem students face when trying to get through exponents.

What happens when you add, multiply, subtract, or divide? What happens when you do a bunch of math and you end up with a square root in the denominator? (Oops, when I wrote this I realized I didn’t teach about denominator-roots in my video! Remind me to teach you that next time, please.)

In this video, and in the subsequent text, I will explain the essential knowledge necessary for square root success on the SAT.

Enjoy:

Square Root Domination

SAT Algebra is hard enough without being forced to remember specific square root rules. The video should have cleared most of your problems up, but I wanted to quickly explain, with written words, how square root addition, subtraction, multiplication, and division work.

If this is too wordy or confusing, watch the video. But I like to provide even more awesome value on this blog that you cannot get on my Youtube channel or otherwise.

Adding and Subtracting Square Roots on the SAT

Adding and subtracting square roots is deceptively easy. Whenever you see a square root, convert it to a variable (so, 3 root 5 should now be 3x)

Whenever you add or subtract, treat the square roots the same way you’d treat the variables.

For example, if you had 3x + 4y, you would not be able to simplify. Your answer would be 3x + 4y. So, if you were to replace your roots with x’s and y’s, and had a value: 3 root 2 + 4 root 5, you wouldn’t be able to minimize that value.

But, if you had 3x + 4x, you could easily combine and get 7x. Thus (you like how I used the thus like some arrogant teacher? Hah!), if you had 3 root 2 + 4 root 2, you’d get 7 root 2.

Cool, huh?

(Note: The same thing works for subtraction. Addition and subtraction are look like that.)

Multiplication and Division on the SAT Algebra

Multiplying and dividing square roots is also relatively easy, if you know what to do. Like with addition, if you apply the “Variable” trick to square roots, you can pretty easily solve the problems:

3√5 * 4√5 = (3 * 4) * (√5  * √5) = (12) * (√25) = (12 * 5) = 60

Whoa! What just happened there?

Well, first of all, you take the numbers and multiply them. Then you take the roots and multiply them as if there was no root sign. Then you just plop that sign right on top, and you have yourself a multiplied square root.

Please watch the video above, as I explain everything very quickly. In the meantime, know that SAT algebra and square roots on the SAT does not have to be difficult.

What do you have trouble with? How can I help you succeed? Please answer in the comments below.

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