Question

Square root of 40 prime factorization radical form

a) 2√10
b) 4√5
c) 2√2√5
d) 8√5/2

Answer 1

The square root of 40, when expressed using prime factorization and radical form, is found by first determining the prime factors, which are 2 x 2 x 2 x 5, and then taking the square root by pairing identical factors. The correct expression in radical form is 2∥10.

Step-by-step explanation:

The student is asking how to find the square root of 40 by using prime factorization and expressing the result in radical form. Let us go through the process step by step.

1. Firstly, we find the prime factors of 40, which are 2 x 2 x 2 x 5 or 23 x 5.
2. To take the square root, we look for pairs of identical factors. The pair of 2's can be taken out of the square root as a single 2, leaving us with 2 x 21∥5.
3. Simplifying further, we take one 2 out as a multiplier, and we are left with 2∥10, which is equivalent to the original option (a).
4. The correct prime factorization of the square root of 40 in radical form is therefore 2∥10.