Question

Which two square roots are used to estimate the square root of 42

Answer 1

Welcome to OpenStudy!

Answer 2

so we need to find out what square root of 42 is in between

so list all the squares of number

can you tell me what these equal to:

2^2 = ?
3^2 = ?
4^2 = ?
5^2 = ?
6^2 = ?
7^2 = ?
8^2 = ?

Answer 3

I'll do a few for you so you see how to do it

2^2 = 2*2 = 4
3^2 = 3*3 = 9
4^2 = 4*4 = 16

can you do the rest? @Mathiscoolitsgreat

Answer 4

25
36
49
64

Answer 5

ok, and in between which two of those numbers is 42 in?

choose one number which is the next number larger than 42, and choose another number which is the next number that is smaller than 42

for example, 36 is the next number after 28, and 25 is the number before 28

Answer 6

in these three numbers

36
49
64

can you tell me which two numbers that 42 is in between?

Answer 7

36 and 49 ?

Answer 8

correct, and so we can find that the square root of 42 has to be in between the square root of 49 and square root of 36

\(\sf\Large \sqrt{36} < \sqrt{42} < \sqrt{49}\)

and can you tell me whether 42 is closer to 49 or closer to 36?

Answer 9

36

Answer 10

correct

and since 42 is practically in between sqrt of 36 and sqrt of 49

but it is a little closer to sqrt of 36

we can estimate that square root fo 42 has to be smaller than 6.5 since it's closer to 6 than it is to 7

note: square root of 36 = 6
square root of 49 = 7

Answer 11

and sqrt of 42 is approximately 6.48

so yay!

Answer 12

Thank you for the help!!

Answer 13

Anytime!

Answer 14

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