Question

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.

Answer 1

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