Question

Rosa, Roberto, Andrea, and Inno find an estimate for . Who has proposed the best solution?

Answer 1

\[\sqrt{10}\]

Answer 2

What are their estimates?

Answer 3

Rosa: "Use\[\sqrt{9}\] and \[\sqrt{25}\] to estimate."

Roberto: "I will use \[\sqrt{4}\] and \[\sqrt{9}\]."

Andrea: "It should be \[\sqrt{11}\] and \[\sqrt{12}\]."

Inno: "Use \[\sqrt{9}\] and \[\sqrt{16}\] to find the estimate

Answer 4

sorry it's long

Answer 5

@meilendurcer What do YOU think the answer is?

Explain your answer.

("I don't know" is not an acceptable response)

Answer 6

to be truthful i was gonna say Roberto

Answer 7

sqrt 4 and sqrt of 9 would be a good method to estimate the sqrt of 5 through 8

Because think, you can evaluate the sqrt of 4 and sqrt of 9, but not sqrt of 5.

So you could say:

Since 5 is inbetween 4 and 9,

the square root of 5 is between the square root of 4 and the square root of 9

\[\sqrt4,\ \sqrt 5,\ \sqrt9\]simplify\[2,\ \sqrt5,\ 3\]So the square root of 5 is somewhere between the values 2 and 3, probably closer to the 2 side.

Answer 8

Notice 10 is not between 4 and 9, so those are not helpful for us if we want to estimate the square root of 10 relative to the square root of 4 and square root of 9.

Answer 9

okay second choice Inno?

Answer 10

@meilendurcer What would you estimate sqrt 10 's value to be

Answer 11

Arrange\[\sqrt9,\sqrt10,\sqrt16\]Simplify\[3,\sqrt10,\ 4\]The term square root of ten is somewhere between 3 and 4, more likely closer to the three value.

Answer 12

Lo and behold, a calculator returns the value of: http://www.wolframalpha.com/input/?i=square+root+of+10

~ 3.16

So you see, we properly estimated the value.

I hope you know understand.