The MCAT, especially the physical sciences section will require you to solve numerous equations and work through different calculations. While many of the math tricks I teach are simply ‘shortcuts' teaching you a faster way to solve a given question, math tricks are even more important when it comes to squares and square roots on the MCAT.

Sure you can multiply a number by itself to find its square, but this can be time consuming and quite tedious. And square roots, these are much more difficult to solve without a calculator, especially when the numbers are presented in scientific notation with very larger or very small powers.

The video below shows you my math tricks for solving MCAT style squares and square roots without a calculator.

## MCAT Math – Squares and Square Roots

(click here to watch on YouTube or catch the video transcript here)

**MCAT Questions Solved in this video:**

**Utilizing Square Roots: **Find the hydronium ion concentration in 0.05 molar solution of acetic acid given an acid dissociation constant of 1.8×10^-5.

**Utilizing Squares: **Find the maximum height a feather can reach f it takes off the ground with an initial velocity of 9.3 x 10^-4 m/s. Ignore air resistance.

**<– Watch Previous Video:**Scientific Notation – Addition / Subtraction / Multiplication / Division

**–> Watch Next Video:**Fractions, Ratios, Percentages and Proportions

**Click HERE**for my FREE MCAT Math Quiz

**This is video 5 in my series on MCAT Math Without A Calculator. Click HERE for the entire series**

Jared says

Hi!

I was wondering what the trick was for sqr roots when the 10 is raised to an odd number?

sharon says

i love how you explaining math. you make it sound so easy. thank you

Cj says

I do not understand the scientific notation. I thought if you move the decimal to the right the exponent moves up and to the left then it moves down. For example 0.05 x 1.8 x10^-5 I got 5×2 x10^-3 but you had 5×2 x10^-7. I do not understand when to make the exponent go up or down?

Jordyn Puccio says

Thank you for making these videos–they are very helpful! I had a question though–why did you keep it 80×10^-8 instead of moving the decimal back so that it was 8.0×10^-7? I thought we had to keep it in that format.

Some Student lost in oblivion says

MCAT math without a calculator has always made me a little weary. This video series has completely alleviated those fears. Thank you so much!

Ayesha says

I really like your teaching methodology…

Uzyr Ahmed (@UzairAhmed_J500) says

Can’t we do it like this? Because in the video you changed power instead of the number.

1) 0.05 x 1.8x 10^ -5

2) 5 x 180x 10^ -5

Daniel says

Hi Leah,

this video is awesome and very helpful. However, there is one aspect I am not sure of. Say I would like to approximate the square root of a number in scientific notation, where the exponent is not even, for example 1*10^-7. Do you know any way out there or would you say it is unlikely to see such a question on the MCAT?

Thanks a bunch, I love your videos.

James says

You’ve been so helpful for my MCAT studying. I’ve relied on using a calculator for far too long, and have forgotten how to do some of the basic math tricks I used to know. Thanks for making these videos free to view. It has made my life much easier, so thank you so very much!

Leah4sci says

Thanks for the feedback James. I’m glad to know that these videos are helping you. The key is to look for logical patterns and trust your brain instead of a calculator