Can an exponent be a negative number?

You already know that an exponent represents the number of times you have to multiply a number by itself. A negative exponent is equivalent to the inverse of the same number with a positive exponent. There is nothing special about solving a problem that includes negative exponentials.

easy dubs we gettin out of the gulag with this one

You are quite the absurd person and I honestly love it

is this 8th-grade math? im in 5th grade:+

That is awesome for you continue to learn ahead

What happens if try to find the the square root of an imperfect square

Most probably it will be an irrational number in which case we can only approximate its value. However, sometimes we can write the radicand as a fraction of two perfect squares. Example: √5.76 = √(576∕100) = √(144∕25) = √(12²∕5²) = 12∕5 = 2.4

wow i never actually thought i would ever understand square roots. but theyre actually kinda easy. (i say that now, of course)

lmao i'm sure it'll get harder for us

I just noticed something really interesting (I think): If I can't remember a square of some numbers (7^2 and 8^2 can be a bit tricky for me for some reason) but I remember the square number of the root that comes before it (6 and 36 in the case I'm trying to find 7^2), I can do 36+6 to make it into 6*7, and then add a 7 to make it into a 7*7. I tried to play around and find a rule and I think I found the formula: n^2 + 2n + 1 = ( n + 1 )^2 (where n is the root number of the square that you do know). if you would visualize the numbers on a grid, the n^2 is the area of the square, while the 2n+1 is the number of the additional units the is added on the side. It's easier to see it on a times table: When looking at 25, the number diagonally next to it is 36. If you count the 'units' (the other multiplies that are on the same axes that leads toward 36 IE: 3,6,9 up to 36 on both sides) they will be the same as the 2n+1. I tried to find a formula for a square of a root that isn't immediately follows the root I know. example: 3^2 = 9, 5^2 = ?. unfortunately I couldn't think on one consistent formula, because there is always a need to add more and (n+1) with more additional 1s the further the number is. does the formula I found have a name? I'm pretty sure I wasn't the first to think of that lol

You can use the pascal's triangle I suppose Edit1: here: https://en.wikipedia.org/wiki/Polynomial_expansion Edit2: Sorry that is not true. That applies to expansions with higher powers, but not between different sqaures. But maybe you can look at sum of squares where ∑x^2 = n(n+1)(2n+1)/6

So, a perfect square is basically the answer to an exponent? (ex. 2^2(4), 12^12(144))

it is an integer with a square root that is also an integer

Main content

Algebra basics

Course: Algebra basics > Unit 1

Lesson 4: Square roots

Square roots of perfect squares

Google Classroom

Learn how to find the square root of perfect squares like 25, 36, and 81.

Let's start by taking a look at an example evaluating the square root of

25

$\sqrt{25} = ?$ ‍

Step 1: Ask, "What number squared equals

25

Step 2: Notice that

5

squared equals

25

$5^{2} = 5 \times 5 = 25$ ‍

The answer

$\sqrt{25} = 5$ ‍

Here's a question to make sure you understood:

How can we be sure that $5$ ‍ is the right answer?

Connection to a square

Finding the square root of

25

is the same as finding the side length of a square with an area of

25

A square with an area of

25

has a side length of

5

Practice Set 1:

Problem 1A

4^{2} =

Reflection question

Which claim shows how square roots work?

Practice Set 2:

Problem 2A

\sqrt{1} =

Practice Set 3:

Problem 3A

\sqrt{121} =

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cyanne.13.edwards
Posted 7 years ago. Direct link to cyanne.13.edwards's post “Can an exponent be a nega...”
Can an exponent be a negative number?
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(77 votes)
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- Joann
  Posted 4 years ago. Direct link to Joann's post “You already know that an ...”
  You already know that an exponent represents the number of times you have to multiply a number by itself. A negative exponent is equivalent to the inverse of the same number with a positive exponent. There is nothing special about solving a problem that includes negative exponentials.
  Button navigates to signup page
  (19 votes)
nimitthnithin
Posted 4 months ago. Direct link to nimitthnithin's post “easy dubs we gettin out o...”
easy dubs we gettin out of the gulag with this one
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(68 votes)
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- Anjali Bliss
  Posted 4 months ago. Direct link to Anjali Bliss's post “You are quite the absurd ...”
  You are quite the absurd person and I honestly love it
  Button navigates to signup page
  (29 votes)
kumaa881
Posted 3 months ago. Direct link to kumaa881's post “the most fun part of khan...”
the most fun part of khan academy is definitely reading the comments...
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- hblowder
  Posted 3 months ago. Direct link to hblowder's post “lol i agree”
  lol i agree
  Comment on hblowder's post “lol i agree”
  (15 votes)
ELLEN
Posted 5 years ago. Direct link to ELLEN's post “is this 8th-grade math? i...”
is this 8th-grade math?
im in 5th grade:+
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(39 votes)
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- thomas tomiwa
  Posted 5 years ago. Direct link to thomas tomiwa's post “That is awesome for you c...”
  That is awesome for you continue to learn ahead
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  (35 votes)
Saaketh Gaddam
Posted 5 years ago. Direct link to Saaketh Gaddam's post “What happens if try to fi...”
What happens if try to find the
the square root of an imperfect square
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(18 votes)
Answer
- Jerry Nilsson
  Posted 5 years ago. Direct link to Jerry Nilsson's post “Most probably it will be ...”
  Most probably it will be an irrational number in which case we can only approximate its value.
  
  However, sometimes we can write the radicand as a fraction of two perfect squares.
  Example: √5.76 = √(576∕100) = √(144∕25) = √(12²∕5²) = 12∕5 = 2.4
  Comment on Jerry Nilsson's post “Most probably it will be ...”
  (29 votes)
nathias.grant
Posted 4 months ago. Direct link to nathias.grant's post “we getting outta the hood...”
we getting outta the hood with this now finna get to college after this
Button navigates to signup pageComment on nathias.grant's post “we getting outta the hood...”
(32 votes)
Answer
minnieli1223
Posted 6 years ago. Direct link to minnieli1223's post “I just noticed something ...”
I just noticed something really interesting (I think):

If I can't remember a square of some numbers (7^2 and 8^2 can be a bit tricky for me for some reason) but I remember the square number of the root that comes before it (6 and 36 in the case I'm trying to find 7^2),
I can do 36+6 to make it into 6*7, and then add a 7 to make it into a 7*7.

I tried to play around and find a rule and I think I found the formula:
n^2 + 2n + 1 = ( n + 1 )^2
(where n is the root number of the square that you do know).

if you would visualize the numbers on a grid, the n^2 is the area of the square, while the 2n+1 is the number of the additional units the is added on the side.

It's easier to see it on a times table: When looking at 25, the number diagonally next to it is 36. If you count the 'units' (the other multiplies that are on the same axes that leads toward 36 IE: 3,6,9 up to 36 on both sides) they will be the same as the 2n+1.

I tried to find a formula for a square of a root that isn't immediately follows the root I know. example: 3^2 = 9, 5^2 = ?.
unfortunately I couldn't think on one consistent formula, because there is always a need to add more and (n+1) with more additional 1s the further the number is.

does the formula I found have a name? I'm pretty sure I wasn't the first to think of that lol
Button navigates to signup pageComment on minnieli1223's post “I just noticed something ...”
(12 votes)
Answer
- Shawn
  Posted 6 years ago. Direct link to Shawn's post “You can use the pascal's ...”
  You can use the pascal's triangle I suppose
  
  Edit1: here: https://en.wikipedia.org/wiki/Polynomial_expansion
  
  Edit2: Sorry that is not true. That applies to expansions with higher powers, but not between different sqaures.
  But maybe you can look at sum of squares where
  ∑x^2 = n(n+1)(2n+1)/6
  Button navigates to signup page
  (4 votes)
maruandtotoro
Posted 7 years ago. Direct link to maruandtotoro's post “So, a perfect square is b...”
So, a perfect square is basically the answer to an exponent? (ex. 2^2(4), 12^12(144))
Button navigates to signup pageComment on maruandtotoro's post “So, a perfect square is b...”
(11 votes)
Answer
- suzannac
  Posted 7 years ago. Direct link to suzannac's post “it is an integer with a s...”
  it is an integer with a square root that is also an integer
  Comment on suzannac's post “it is an integer with a s...”
  (11 votes)
Mikaela Matrille
Posted 4 months ago. Direct link to Mikaela Matrille's post “wow i never actually thou...”
wow
i never actually thought i would ever understand square roots. but theyre actually kinda easy. (i say that now, of course)
Button navigates to signup pageComment on Mikaela Matrille's post “wow i never actually thou...”
(14 votes)
Answer
- Dont_Think
  Posted 3 months ago. Direct link to Dont_Think's post “lmao i'm sure it'll get h...”
  lmao i'm sure it'll get harder for us
  Comment on Dont_Think's post “lmao i'm sure it'll get h...”
  (3 votes)
AdalineO
Posted 7 months ago. Direct link to AdalineO's post “How are you doing?”
How are you doing?
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(9 votes)
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- MasonK
  Posted 7 months ago. Direct link to MasonK's post “terrible math dumb”
  terrible math dumb
  Comment on MasonK's post “terrible math dumb”
  (11 votes)