Answer:
13)
Exact solutions: [tex]\pm \sqrt{7}[/tex]
Approximate solutions: [tex]\pm 2.6[/tex]
12)
2 is closer to 1.9881 than to 2.0164, so [tex]\sqrt{2}\approx[/tex] 1.41 .
The number line dot should be closer to 1.4 .
Step-by-step explanation:
13) Let [tex]a[/tex] be real positive or zero number.
[tex]x^2=a[/tex] implies [tex]x=\pm \sqrt{a}[/tex].
You are asked to solve [tex]x^2=7[/tex].
The solution is [tex]x=\pm \sqrt{7}[/tex].
Put into calculator to get what [tex]\sqrt{7}[/tex] is approximately.
[tex]\sqrt{7}\approx 2.6[/tex]
So the approximate solutions to [tex]x^2=7[/tex] is [tex]\pm 2.6[/tex].
Basically the inverse operation of squared is square root.
12)
[tex]1.41^2=1.9881[/tex] by calculator.
[tex]1.42^2=2.0164[/tex] by calculator.
[tex]1.43^2=2.0449[/tex] by calculator.
We need to figure out which of the outputs above is closer to 2.
[tex]|2-1.9881|=0.0119[/tex]
[tex]|2-2.0164|=0.0164[/tex]
[tex]|2-2.0449|=0.0449[/tex]
So 2 is closer to 1.9881 which means [tex]\sqrt{2}[/tex] would be closer to [tex]1.41[/tex].
So anyways let's fill the blanks.
2 is closer to 1.9881 than to 2.0164, so [tex]\sqrt{2}\approx[/tex] 1.41 .
