Question

which number has the greatest value?
a 3.5
b square root of 15**
c square root of 1/16
d 26/100
which number is an irrational number?
a 3.5
b square root of 36
c square root of 48
d 37/100***

If a is a rational number and b is an irrational number, then the sum a + b is
A)rational.
b) imaginary***
C)irrational.
D)an integer.
someone please check my answers asap thanks

Answer 1

ms.sue please help

Answer 2

For the first problem just use a calculator to convert everything into decimals.

a= 3.5
b = sqrt(15) =3.87
c = sqrt(1/16) = .25
d = 26/100 = .26

It's clear after converting everything, that choice b is the greatest

Numer 2: Irrational numbers are numbers that cannot be expressed as fractions.

a=3.5 < --- can be expressed as a fraction (7/2)
b = sqrt(36) = 6 < --- can be a fraction (6/1)
c = sqrt(48) = 6.928 <--- CANNOT be a fraction
d = 37/100 <--- its already written as a fraction

So choice c is irrational

Number 3:
The sum of a rational number and irrational number is irrational.

If you add 6 which is a rational number to irrational number such as square root of 48:

6+6.928 = 12.928

And you cannot express that as a fraction, so it's irrational.