DB225: Maths for Diploma Studies: Roots Reinforcement Questions

Roots Reinforcement Questions

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.

What is the 4^th root of 86?

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

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

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!

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.

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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Maths for Diploma Studies

Roots Reinforcement Questions

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