A radical that has 2^2 and 5 as factors could be 5√2, so option A is a possible match.
To find another possibility, we need to simplify 20√5 further. We can simplify the √5 part by noticing that 5 is a perfect square factor, so we can write:
20√5 = 4 * 5 * √5 = 2^2 * 5 * √5
Now we need to find a radical that has 2^2 * 5 as factors. Option B has 200 (which is 2^3 * 5^2) as a factor, but it also has an extra factor of 5 that we don't need.
Option C has -20 and √50, but we can simplify √50 to 5√2, which gives us:
-20√50 = -20 * 5√2 = -100√2
This is not a match either, so we move on to option D. This has -20 and √125, and we can simplify √125 to 5√5:
-20√125 = -20 * 5√5 = -100√5
This is a match! So the two possible radicals that can be a like radical to 20√5 are:
Answers & Comments
Answer:
which TWO radicals can be a like eadical to 20√5?
a.5√2
b.200√25
c.-20√50
d.-20√125
e 3√20
Answer:
The prime factorization of 20√5 is 2^2 * 5 * √5.
A radical that has 2^2 and 5 as factors could be 5√2, so option A is a possible match.
To find another possibility, we need to simplify 20√5 further. We can simplify the √5 part by noticing that 5 is a perfect square factor, so we can write:
20√5 = 4 * 5 * √5 = 2^2 * 5 * √5
Now we need to find a radical that has 2^2 * 5 as factors. Option B has 200 (which is 2^3 * 5^2) as a factor, but it also has an extra factor of 5 that we don't need.
Option C has -20 and √50, but we can simplify √50 to 5√2, which gives us:
-20√50 = -20 * 5√2 = -100√2
This is not a match either, so we move on to option D. This has -20 and √125, and we can simplify √125 to 5√5:
-20√125 = -20 * 5√5 = -100√5
This is a match! So the two possible radicals that can be a like radical to 20√5 are:
A. 5√2 D. -20√125