Question 1

When doing prime factorisation to get all perfect squares out of a square root, how do you decide which prime to factor out by?

Accepted Answer

I don't know what you mean by "how do you decide which prime to factor out by??
1)  Are you asking how do you start the prime factorization?  You can start anywhere.  you need any 2 numbers that multiply to the original number, and then keep factoring until you get the prime factors   
2)  Or, are you asking how do you know which prime factors are perfect squares?  Any prime factor that occurs twice (is squared), is a perfect square.

If this doesn't answer your question, comment back and please clarify your question.

Question 2

Hey guys,106jmb i saw your question. I saw a faster way to find cube roots.

We already know some basic cube numbers

0^{3}0 
3
 =0

1^{3}1 
3
 =1

2^{3}2 
3
 =8

3^{3}3 
3
 =27

4^{3}4 
3
 =64

5^{3}5 
3
 =125

6^{3}6 
3
 =216

7^{3}7 
3
 =343

8^{3}8 
3
 =512

9^{3}9 
3
 =729

Now, the common thing here is that each ones digit of the cube numbers is the same number that is getting cubed , except for 2 ,8 ,3 ,7 .

now let us take a cube no like 226981 .

to see which is the cube root of that number , first check the last 3 digits that is 981 . Its last digit is 1 so therefore the last digit of the cube root of 226981 is 1 .

Now for the remaining digits that is 226

Now 226 is the nearer & bigger number compared to the cube of 6 (216)

So the cube root of 226981 is 61

Let us take another example - 148877

Here 7 is in the last digit but the cube of seven's last digit is not seven. But the cube of three has the last digit as 7.

So the last digit of the cube root of 148877 is 3.

Now for the remaining digits 148.

It is the nearer and bigger than the cube of 5 (125).

Therefore the cube root of 148877 is 53.

Let us take another example 54872.

Here the last three digit's (872) last digit is 2 but the cube of 2's last digit is not 2 but the last of the cube of 8 is 2.

So the last digit of the cube root of 54872 is 8.

Now of the remaining numbers (54). It is nearer and bigger to the cube of 3 (27). So therefore the cube root of 54872 is 38.

Accepted Answer

i also use this method!

Question 3

I use Kumon as well as Khan Academy, and they are attempting to teach me a method I don't understand and can't find anywhere else. This is the procedure:

to find the square root of 3969:
1. Divide the radicand into groups of two digits, starting from the right side.
2. Find the number that is closest to but less that 39 when squared
3. Write the number found in step (2) twice and find the sum.
4.find the number, x, that is closest to but less than or equal to 369 when sustituted into 12x*x.
5. Write the number found in step (4)

Have you heard of this method before and if so can you explain it, please?

Accepted Answer

Idk what you thinking but Kumon does not teach anyone

Question 4

can negative integers have square and how

Accepted Answer

Yes, negative integers can have square roots. The topic is imaginary numbers. For example, i^2=-1. If you want to learn more about this, you can search up imaginary numbers on Khan Academy and watch videos on them.

Question 5

How do you solve an equation with a square root in it

Accepted Answer

Good question!

Generally, a square root equation is solved by isolating the square root (or radical), squaring both sides to get rid of the square root, and then solving the resulting equation.  Solutions *must* be checked by substituting them into the *original* equation, because squaring both sides can create extraneous (invalid) solutions.

Example: Solve sqrt(x) + x = 0.
sqrt(x) = -x
x = x^2
0 = x^2 - x
0 = x(x - 1)
x = 0 or x - 1 = 0
x = 0 or x = 1

Check: sqrt(0) + 0 = 0 + 0 = 0, so x = 0 is a valid solution.
sqrt(1) + 1 = 1 + 1 = 2, which is not 0, so x = 1 is an extraneous (invalid) solution.

So the only solution is x = 0.

Have a blessed, wonderful day!

Question 6

I need help this is very challanging!

Accepted Answer

Is  there anything specific you don't understand?

Question 7

Do you know cube roots

Accepted Answer

★*Finding the cube root is similar to finding the square root*, _but instead of grouping primes in twos, *group matching primes by three*_, because instead we're looking for what the third power root is.

No matter which prime you start with, the number will break down to the same primes.

*Cubed root of 64*?
```   *64*
    /\
*2* • 32
      /\
  *2* • 16
        /\
    *2* • 8
          /\
      *2* • 4
            /\
         *2* • *2*```

•There are six 2s.
2 • 2 • 2 • 2 • 2 • 2 = 64

Which *group by three _twice*_.
(2 • 2 • 2) • (2 • 2 • 2)

•*Take one representative _from each matching prime group*_, and multiply.

2 • 2 = *4*←the root! 🥳
this tells us…

★_*The cubed root of 64 is 4*_.
because four cubed, 4^3 = 64

★*All the roots work this way*…
• find the prime factors
• group _matching primes_ by the indexed number
• take one representative from each group and multiply them

So if we need to find the 5th root, _the matching primes would be grouped five each_.

(≧▽≦) I hope this helps!

Question 8

4 square root 3 squared

Accepted Answer

That could be interpreted in two ways
4 (srt(3))^2 = 4*3=12
(4 sqrt(3))^2=16*3=48.

Question 9

Who created square roots and why is it a thing?

Accepted Answer

No one actually knows who invented the square root, but it is thought that the knowledge of square roots originally came from dividing areas of land into equal parts so that the length of the side of a square became the square root of its area

8th grade

Course: 8th grade > Unit 1

Square roots review

Square roots

Finding square roots

Practice

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