Answer:
Jaclyn's reasoning is incorrect. 7.1 is the correct answer.
Step-by-step explanation:
Jaclyn estimates the square root of 50 in the following way:
[tex]\sqrt{50}=2\sqrt{(25)}=2=10[/tex]
(a) Jaclyn's reasoning is incorrect because she has taken square root of 25 and multiplied by 2 while [tex]\sqrt{50}[/tex] should be equal to 5√2.
(b) [tex]\sqrt{50}[/tex]
Write 50 as its prime factors.
[tex]\sqrt{2\times 5\times 5}[/tex]
Group the same prime factors in to pairs
[tex]\sqrt{(5\times 5)\times 2}[/tex]
rewrite each pair in exponent form
[tex]\sqrt{5^{2}(2)}[/tex]
Use this rule [tex]\sqrt{x^{2} }=x[/tex]
[tex]5\sqrt{2}[/tex] = 7.07 rounded to 7.1
