Question

Jaclyn estimates that the square root of 50 in the following way:

50 −−−√ = 225−−√ =2*5 = 10
Explain why her reasoning is incorrect. Please use complete sentences.

(2 points for explaining why it is wrong, 1 point for writing in complete sentences.)

Answer 1

5(√) = 7.071

Explanation:

Answer 2

Her reasoning is wrong because she forgot the root of 2. (
`√(2)`)

Explanation:

We decompose the number into prime factors

50 = 2*25 = 2*5*5 = 2*(5^2)

Now, we apply the square root of the last term

`√(2*5^2)`

This is equal to:

`√(2)`*
`√(5^2)` =

`√(2)`*5 = 5
`√(2)` = 7.071

Which is the same answer as
`√(50)` = 7.071