how do you simplify radicals?

Question

like is there an easy way to know how to simplify

√20
√72

Answer 1

√20 = √(4 x 5) = 2√5
√72 = √(36 x 2) = 6√2

Answer 2

20 = 5*4
so √20 = √5*4
but 4 is a perfect square and can be brought out of the radical to get 2√5

also, 72 = 9*8 = 9*4*2
so √72 = √9*4*2
but again, 4 is a perfect square and so is 9
so √72 = (2*3)√2 = 6√2

Answer 3

u take the number for example 20:
u divide it by the first small divisor ex: for 20 its 2
u will have 10 for 10 its also 2 ul have 5 for 5 its five ul have 1 then its done
this way it should be written:
20|2
10|2
5|5
1
because ur radical is base 2 u take the pairs and count them as 1 outside the radical in the case of 20:
u have 2*2*5=2V5
the pair of twos is taken as a 2 outside the radical and the 5 stays in

for 72:

72|2
36|2
18|2
9|3
3|3
1
2*2*2*3*3 here we have a pair of threes and a pair of twos and a single 2 its written as : 2*3V2=6V2


hope ul understand good luck :D

Answer 4

Yes. 20, for example. If 20 equals 5 times 4, then you can take the square root of 4 (which is 2) and put it in front of the radical. so you would have 2 outside the radical sign and 5 inside. I'm pretty sure, at least! hope that helped some.

Answer 5

Basically you want to separate the radical into square numbers.

sqrt (20) = sqrt (4 x 5)

four is a square number so you can pull it out and put the square root of 4 (which is 2) outside the radical

sqrt (20) = 2 x sqrt(5)

do the same for sqrt(72)

sqrt(72) = sqrt (36 x 2)

sqrt(36) is 6 so pull that out and you get:

sqrt(72) = 6 x sqrt(2)

Answer 6

Find multiples
For example simplify (20)^(1/2) to (5*4)^(1/2)
This can further split up to 5^(1/2)*4^(1/2)
We know that the square root of 4 is equal to 2
So, our answer would be 2(5)^(1/2)

Answer 7

Look for any squares within the factors of the number:
sqrt(20)
sqrt(4 x 5)
sqrt(4) * sqrt(5)
2√5

sqrt(72)
sqrt(4 * 9 * 2)
sqrt(4) * sqrt(9) * sqrt(2)
2 * 3 * sqrt(2)
6√2

Answer 8

You need to find the largest complete square that is a multiple of the number.

For example,
sqrt(20) = sqrt(4*5) = sqrt(4) * sqrt(5) = 2*sqrt(5)

Answer 9

Sqrt(12) = 2 * Sqrt(3) - 4 * Sqrt(27) = - 4 * 3 * Sqrt(3) + 2 * Sqrt(75) = + 2 * 5 * Sqrt(3) Add them up and you get (2 - 12 + 10)*Sqrt(3) = 0

Answer 10

square root of 20 is this square root of 4*5
You can take the square root of 4
so you end up with 2 square root of 5

square root of 72 is this square root of 8*9
4*2*9

You can take the square root of 4 and 9
so you end up with 6 square root of 2