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.

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

the answer Part b) is 8.5