Question

Simplify 5√3•4√3=

Answer 1

string of multiplication
\[5 * \sqrt{3} * 4 * \sqrt{3}\]

Answer 2

And

Answer 3

remember a square root is the same as raised to 1/2 power

root 3 times root 3 will cancel the square root,

\[\large \sqrt{x}*\sqrt{x} = [\sqrt{x}]^2 = x^{(1/2)*2} = x\]

Answer 4

so you just get 5 * 4 * 3

Answer 5

OH so that's all

Answer 6

How about this one
√8•6√5

Answer 7

DanJs can you please help me with the rest

Answer 8

yeah, you can combine those roots since they are multiplied

6*root(8*5)

6* root(40)

simplify the root 40

Answer 9

How do I simplify root 40

Answer 10

6* root(4 * 10) = 6* root(4) * root(10) = 6 * 2 * root 10

12*root(10)

Answer 11

break it up into any squares it may contain , here 4 * 10 = 2^2 * 10,

Answer 12

you can pull that 2 out front root 2^2 = 2

Answer 13

break the numbers into their prime factors, and take out any perfect squares you can, if any

Answer 14

Thank you I also have two more I really don't understand anything about roots

Answer 15

If u can help with these

Answer 16

To make the first equation simpler to understand, let ignore the root by letting x=root(5)
What would the answer be for 3x+ 11x-x ?

Answer 17

14x-x

Answer 18

yes but what is 14x - 1x ?

Answer 19

13x

Answer 20

correct now recall x = root(5) so substitute x back into your equation to get the final answer

Answer 21

How do I do that

Answer 22

where you see an x, replace it with a root(5)

Answer 23

So is my answer 13√5

Answer 24

a simpler way to do the first equation is to factor out the root(5) such that
3root(5) + 11root(5) - root(5) = (3 +11 -1)root(5) = 13root(5)

Answer 25

yes

Answer 26

Ok thank you so much what about the second equation

Answer 27

simplify the first two terms and way DanJS showed you and sum the terms. Look for a common root for all three terms.

Answer 28

I don't get it

Answer 29

Root 3

Answer 30

break the numbers into their prime factors, and take out any perfect squares you can, if any per DanJS

Answer 31

I don't know how to break the numbers into their prime factors

Answer 32

do you know what prime factors are?

Answer 33

Yeah I do but what about the 3

Answer 34

3 is a prime number

Answer 35

So what's next

Answer 36

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly.

Answer 37

What are the prime factors for 12?

Answer 38

2 6
2 3

Answer 39

Your close what are the prime factors of 6 ?

Answer 40

2 3

Answer 41

Yes, so the prime factor of 12 is 2, 2 and 3 such that if I take 2 x 2 x 3 I get 12.
This is the same as 2^2 x 3 = 12

break the numbers into their prime factors, and take out any perfect squares you can, if any per DanJS

The perfect square is the 2^2 or 4

Answer 42

So what's my final answer

Answer 43

so to simplify root(12) = root(4) times root(3)
the square root of 4 is 2

so root(12) is 2root(3)

Now you have to simplify root(27) by the same method

then add all 3 terms with the common root

Answer 44

Can you demonstrate it please

Answer 45

figure out the prime factors in 27 find a perfect square and add the terms

Answer 46

27
9 3
3 3

Answer 47

yes, when you are adding together terms containing roots, the stuff under the root has to be the same
you cant add root(2) to root(5) for example,

Answer 48

so really you may not be able to simplify at all maybe, follow what you did with the factoring first

Answer 49

\[\sqrt{12}=\sqrt{3*4}=\sqrt{3*2*2} = \sqrt{3*2^2} = \sqrt{3}*\sqrt{2^2} = 2*\sqrt{3}\]

Answer 50

27 = 9 * 3 = 3 * 3 * 3 = 3^2 * 3

root(27) = root(3^2)*root(3) = 3*root 3

Answer 51

all are multiples of root 3 now, you can total them up

Answer 52

So what's my answer going to be

Answer 53

\[2\sqrt{3}-3\sqrt{3}+\sqrt{3}\]


2 -3 + 1 or 0*root(3) = 0

Answer 54

simplifies to zero

Answer 55

Yeah so what do I write

Answer 56

Just zero