Question

1. Is the product of √16 and 4/7 rational or irrational? Explain your reasoning.

2. The product of √576 and √684 is:
A irrational because both factors are irrational
B rational because both factors are rational
C irrational because one factor is irrational
D rational because one factor is rational
3. A teacher wrote the following set of numbers on the board:
a = √20 b = 2.5 c = √225
Explain why a + b is irrational but b + c is rational.
4. Jakob is working on his math homework. He decides that the sum of the expression
1/3 +6√5/7 must be rational because it is a fraction. Is Jakob correct? Explain your reasoning.

Answer 1

1. Irrational

2. C irrational because one factor is irrational

Explanation:

1. Product of √16 and 4/7

=
`√(16)*(4)/(7)`

⇒
`4*(4)/(7)=(16)/(7) =2.28571428571`

which is an irrational number because numbers after the decimal is repeating and non-terminating.

2. Product of √576 and √684

= √576 × √684

= 24 × 6√19 = 144√19 which is an irrational number.

Thus, option C is correct.

3. Given, a = √20 b = 2.5 c = √225

Then, a + b = √20 + 2.5 = 2√5 + 5.5

which is an irrational number because √5 is an irrational number.

Also, b + c = 2.5 + √225 = 2.5 + 15 = 17.5

which is rational number because decimal is terminating and non-repeating.

4.
`(1)/(3) +(6√(5) )/(7) = (7+18√(5) )/(21)`

which is an irrational number because fraction include √5 also.

Thus, Jacob is not correct.

Answer 2

1) Rational because the square root of 16 is 4 and 4 times 4/7 is a rational number (16/7)

2) Irrational because square root of 684 is irrational C

3) The square root of a is irrational so the answer is irrational. The square root of c is rational so the answer is rational.

4) Jacob is wrong because the square root of 5/7 is irrational so the answer to the problem is irrational.