Question

Describe how you would estimate the square root of a number that is not a perfect square without using a calculator.

Answer 1

i need the answer lol

Answer 2

well what if you found perfect squares that this non perfect number is inbetween

Answer 3

I would .... I'm not sure I'm not good at math.

Answer 4

alright so say you have a number 7...

Answer 5

so \[\sqrt{7}\]it is not the perfect square however 4 and 9 are

Answer 6

and we know that it's square root is greater than square root for 4 and less than 9

Answer 7

\[\sqrt{4}<\sqrt{7}<\sqrt{9}\]
\[2<\sqrt{7}<3\]

Answer 8

thank you

Answer 9

so now we know that it's between 2 and 3, take the number that it between the two outer numbers 9-4=5 ... use this as a partitions in that difference between 2 and 3 (1). This means that each partition is .2 (1/5). since there is a difference of 3 additions of 1, you'd add 3 .2's to the number

Answer 10

so my estimate would be

\[\sqrt{7}=2.6\]

Answer 11

the actual is
\[sqrt{7}=2.64\]

Answer 12

Thank you so much