Surrds Question?

Question

Can you expalin how you would simplify "square root of 20" or the "square root of 32"???

Thanx!

Answer 1

The point of simplifying surds is to get the smallest number inside the square root.

root 20 is the same as the square root of 4 * the square root of 5. Since root 4 is a rational number (it's 2), you can simplify the equation to get 2 root 5 (as in "the square root of 5, multiplied by 2").

For root 32, you would do the same thing. Divide it by two, to get root 16 * root 2. Root 16 can be simplified to 4, so you've got 4 root 2.

Hope this helps!
(Man, this is hard without proper mathematical notation :/ )

Answer 2

yes you divide the number by something that can be squared so simplified root of 20 would be 4*5 so square root of 4 is 2 so it would be 2 square root of 5

Answer 3

√20 = √(4 x 5) = 2.√5
√32 = √(16 x 2) = 4.√2

Answer 4

I think they may be asking how to write it more simply, i.e. the square root sign followed by 20 (or 32)

Answer 5

Write it as a product of its factors.
20 = 4*5 = 2^2 * 5
sqrt(20) = 2*sqrt(5)

Do same thing for 32.

Answer 6

memorize this rule sqrt(a^2) = a (assume a is positive)

sqrt(20)

prime factor
sqrt(2x2x5)

sqrt(2^2 x 5)

sqrt(2^2) * sqrt(5)

2sqrt(5)
------------------

sqrt(32)

sqrt( 2x2x2x2x2)

sqrt(4 x 4 x 2)

sqrt(4^2 x 2)

sqrt(4^2) * sqrt(2)

4sqrt(2)

hope this helps

Answer 7

sqrt 20 = sqrt(4x5) = 2sqrt5

sqrt 32 = sqrt(16x2) = 4sqrt2