Jamelia estimates the square root of 72 in the following way: √72 = 2√36 = 2*6 = 12(a) Explain why her reasoning is incorrect.(b) Estimate the square root of 72 to the nearest tenth. Show your work.
Accepted Solution
A:
Part a) we have that √72 √72-----> √(2*36)=√2*√36 is not 2*√36------> this is the error √2*√36=√2*√6²-----> √2*(6)----> 6√2
alternative method 72 is equal to-------> 2³*3² therefore √72-----> √[2³*3²]----->√ 2³*√3²-------> (2√2)*(3)-----> 6√2
Part b)Estimate the square root of 72 to the nearest tenth
we know that √2 is equal to 1.41 so √72=6√2------> 6*1.41-----> 8.46----> 8.5