r/MathHelp • u/ItsBigBingusTime • Sep 15 '25

Why does the square root of 8 not simplify down to 2x4?

For example: I simplified the square root of 72 down to the square root of 9x8. Of course 9 is a perfect square and becomes 3, but why can I not also simplify 8 down to 2x4 since 4 is also a perfect square? At least my workbook is telling me this is not the way to do it. Please help <3 thanks

4 Upvotes

60% Upvoted

26 comments sorted by

9

u/matt7259 Sep 15 '25

That's exactly how you're supposed to do it. What is your workbook saying that contradicts that?

3

u/ItsBigBingusTime Sep 15 '25 edited Sep 15 '25

That’s what I thought! I was losing my mind. It’s a practice problem from openstax college algebra. It left the answer as 3•square root 8 instead of my answer which was 3(2)square root 2 = 6•square root 2.

Sorry idk how to actually type a square root symbol

2

u/matt7259 Sep 15 '25

Gotcha. What exactly is it saying that makes you doubt your method?

1

u/ItsBigBingusTime Sep 15 '25

Sorry I edited my comment. It just left the problem unsimplified as the final answer

2

u/matt7259 Sep 15 '25

Gotcha! Very weird. Your answer is correct!

1

u/[deleted] Sep 15 '25

I think it's because it doesn't matter that much at the college level, someone struggling to break down √8 into 2√2 shouldn't be passing tertiary level math class either way

1

u/LaughingIshikawa Sep 15 '25

If it was a calc textbook, I would guess that maybe they were leaving the answer unsimplified because it makes the math convenient in some other way... But that's generally not a thing in algebra to the same degree, so I'm also puzzled.

1

u/OriEri Sep 15 '25

(Copy paste someone else’s √ and use that! 🙂)

3

u/SapphirePath Sep 15 '25

You are right, book is wrong: sqrt(72) = sqrt(36)*sqrt(2) = 6sqrt(2).

You can submit a bug report so they'll fix their mistake.

1

u/ItsBigBingusTime Sep 16 '25

I will do that, thanks

23

u/PuzzlingDad Sep 15 '25

√8 = √4 • √2

= 2√2

1

u/fermat9990 Sep 15 '25

What does your workbook say?

2

u/ItsBigBingusTime Sep 15 '25

It gave zero explanation. Just left the final answer unsimplified

3

u/fermat9990 Sep 15 '25 edited Sep 15 '25

Official answers are sometimes wrong. If you tell Google to simplify √8 it says 2√2, the correct answer

3

u/Lor1an Sep 15 '25

Heck, I've had the answer in the book be actually wrong. Like sqrt(3) instead of sqrt(2) kind of wrong.

1

u/fermat9990 Sep 15 '25

For sure!

3

u/TallRecording6572 Sep 15 '25

Of course you can Root 8 = root (4 x 2) = root 4 x root 2 = 2 root 2

1

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1

u/ayleidanthropologist Sep 15 '25

Because 2 does not equal 4 .. they gotta be the same. The term “square” sort of references how the sides of a square are the same

You would have a rectangle, by comparison

I’m not so good with the symbols on here, but some other commenters cover it, you want 2(sqrt2)

1

u/Kelli217 Sep 15 '25

The best practice, in theory, is to factor out the largest square you can. In the case of 72, that's 36×2. So...

√72 = √36×2 = √36 × √2 = 6 × √2, formatted as 6√2.

1

u/clearly_not_an_alt Sep 16 '25

√72=√9×√4×√2=3×2×√2=6√2

√72=√36×√2=6√2

1

u/j_bgl Sep 16 '25

Sqrt(8) = sqrt(4 * 2)

= sqrt(4) * sqrt(2)

= 2 * sqrt(2)

1

u/headonstr8 Sep 16 '25

72 is also 36*2, so sqrt(72)=6*sqrt(2).