Roots Reinforcement Questions

1.

Your friend asks you what the square root of -4 is. What do you tell them?

a)    There isn’t one

b)    -2

c)    2

d)    -4

Since a negative number multiplied by a negative number is a positive number, if you were to square -2, you would get 4. So -4 doesn’t have a square root. So option a is the correct one. 

2.

What is the 4th root of 86?

This is simple, but it’s a job for a scientific calculator:

begin mathsize 14px style fourth root of 86 space equals space 3.045 end style

3.

What is the answer to the equation below?

ln (2.71834)

There are two ways of doing this. One is to calculate 2.71834 and then take a natural log of result:

begin mathsize 14px style 2.718 to the power of 34 space equals space 583 comma 461 comma 742 comma 527 comma 454.88 end style

begin mathsize 14px style l n space left parenthesis 583 comma 461 comma 742 comma 527 comma 454.88 right parenthesis space equals space 34 end style

The other is to remember that the natural log base (e) = 2.718 and taking a logarithm of a number tells us the exponent that the base is raised by to get the result!

4.

Which of these are the same number?

begin mathsize 14px style 25 squared space cross times space 25 space a n d space 25 cubed end style

begin mathsize 14px style 353 space cross times space 3 space a n d space 354 end style

begin mathsize 14px style cube root of 6 space a n d space space fourth root of 12 end style

begin mathsize 14px style 12 cubed space minus space square root of 144 space cross times space 2 end root space a n d space 1442 space minus space 122 end style

Only 252 × 25 and 253 are the same number because 252 is 25 × 25 and 253 is 25 × 25 × 25.

5.

What is begin mathsize 14px style open parentheses 23 squared space x space 12 to the power of negative 2 end exponent close parentheses space plus space square root of 14 end style?

This is straightforward:

begin mathsize 14px style 23 squared space equals space 529 end style

begin mathsize 14px style 12 to the power of negative 2 end exponent space equals space 0.00694 end style

begin mathsize 14px style square root of 14 space equals space 3.74 end style

So it’s just:

begin mathsize 14px style left parenthesis 529 space cross times space 0.00694 right parenthesis space plus space 3.74 end style

begin mathsize 14px style 3.67 space plus space 3.74 space equals space 7.41 end style

Next, we get into orders of magnitude

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