Question

A. Evaluate x^2 when x = 7.

b. Evaluate √x when x = 81.
c. Evaluate x^3 when x = 5.
d. Evaluate √x when x = 27.

Answer 1

b. 2 (square root) 2 (decimal form ( 2.8284...))

C. ???

D. 3 (square root) 3

Explanation:

Answer 2

a)
`49`

b)
`9`

c)
`125`

d)
`3√(3)`

Explanation:

a. Evaluate x^2 when x = 7.

saying
`x^2` is the same as saying
`x * x`

so, when
`x=7`, it means
`7 * 7`

`7^2`

`7 * 7`

`49`

b. Evaluate √x when x = 81.

`√(x)` is the opposite of
`x^2`. 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
`x^2` then the square root shows that the number
`x` multiplied with itself twice to make
`x^2`. Hence
`√(x * x)\,\text{is}\,x`

`√(x* x) = √(x^2) = x`

------------

we know that
`9 * 9\,\text{is}\,81`

we can write

`√(81)`

`√(9 * 9)`

`9`

c. Evaluate x^3 when x = 5.

Just as
`x^2 = x*x`

similarly,
`x^3 = x*x*x`,

so when x=5.

`x^3 = x*x*x`

`5^3 = 5*5*5`

`125`

d. Evaluate √x when x = 27.

We know that
`x = 27`,

we also know that
`x = 3*9`

we break this further
`x = 3*3*3`

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.

`√(x) = √(3*3*3)`

we're only going to select two 3's within the square root and reveal the answer.

another to think about this is:

`√(x) = √(9*3)`

9 is a number that is 3 x 3 hence
`sqrt{9} = 3`

so our answer will be:

`√(x) = 3√(3)`