When square root of 2800 is written as a mixed radical in form of a radical b, the value of ab is
A) 7
B) 27
C) 140
D) 280
I square root and simply it and got the answer 20 radical 7. But how do I find the value of ab
well, 2800 is 20^2 * 7 so ab = 140
To find the value of ab, we need to break down the square root of 2800 into its factors and simplify it.
Start by finding the prime factorization of 2800:
2800 = 2 * 2 * 2 * 5 * 5 * 7
Now, group the factors in pairs, taking one factor from each pair. Since we're looking for a mixed radical form, we want to find the largest perfect square that divides evenly into 2800. In this case, it's 4 because 2*2 = 4.
So, we can rewrite 2800 as:
2800 = 4 * (2 * 2 * 5 * 5 * 7)
Now, simplify the square root of each perfect square and bring them out of the square root symbol:
sqrt(2800) = sqrt(4) * sqrt(2 * 2 * 5 * 5 * 7)
The simplified form is:
2 * 5 * sqrt(2 * 7) = 10 * sqrt(14)
Comparing the expression to the form "ab":
a = 10
b = sqrt(14)
To find the value of ab, multiply a and b:
ab = 10 * sqrt(14)
So, the value of ab is 10 * sqrt(14).
Since none of the answer choices matches this result, there might be an error in the options provided or the given question. Please double-check the options or reconfirm the question.