Answer:
a) [tex]49[/tex]
b) [tex]9[/tex]
c) [tex]125[/tex]
d) [tex]3\sqrt{3}[/tex]
Step-by-step explanation:
a. Evaluate x^2 when x = 7.
saying [tex]x^2[/tex] is the same as saying [tex]x \times x[/tex]
so, when [tex]x=7[/tex], it means [tex]7 \times 7[/tex]
[tex]7^2[/tex]
[tex]7 \times 7[/tex]
[tex]49[/tex]
b. Evaluate √x when x = 81.
[tex]\sqrt{x}[/tex] is the opposite of [tex]x^2[/tex]. It shows that, if there's a number 81, then what number multiplied with itself twice to make 81?
----------
More generally, if there's a number [tex]x^2[/tex] then the square root shows that the number [tex]x[/tex] multiplied with itself twice to make [tex]x^2[/tex]. Hence [tex]\sqrt{x \times x}\,\text{is}\,x [/tex]
[tex]\sqrt{x\times x} = \sqrt{x^2} = x[/tex]
------------
we know that [tex]9 \times 9\,\text{is}\,81[/tex]
we can write
[tex]\sqrt{81}[/tex]
[tex]\sqrt{9 \times 9}[/tex]
[tex]9[/tex]
c. Evaluate x^3 when x = 5.
Just as [tex]x^2 = x\timesx[/tex]
similarly,[tex]x^3 = x\timesx\timesx[/tex],
so when x=5.
[tex]x^3 = x\timesx\timesx[/tex]
[tex]5^3 = 5\times5\times5[/tex]
[tex]125[/tex]
d. Evaluate √x when x = 27.
We know that [tex]x = 27[/tex],
we also know that[tex]x = 3\times9[/tex]
we break this further[tex]x = 3\times3\times3[/tex]
the square root takes shows the number that multiples with itself twice
Here we 3 multiplying itself three times within the square root!
but no worries, we're only going to take two 3's from here.
[tex]\sqrt{x} = \sqrt{3\times3\times3}[/tex]
we're only going to select two 3's within the square root and reveal the answer.
another to think about this is:
[tex]\sqrt{x} = \sqrt{9\times3}[/tex]
9 is a number that is 3 x 3 hence [tex]sqrt{9} = 3[/tex]
so our answer will be:
[tex]\sqrt{x} = 3\sqrt{3}[/tex]
Answer:
b. 2 (square root) 2 (decimal form ( 2.8284...))
C. ???
D. 3 (square root) 3
Step-by-step explanation:
