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.
Answer:
1. Irrational
2. C irrational because one factor is irrational
Step-by-step explanation:
1. Product of √16 and 4/7
= [tex]\sqrt{16}\times\frac{4}{7}[/tex]
⇒ [tex]4\times\frac{4}{7}=\frac{16}{7} =2.28571428571[/tex]
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. [tex]\frac{1}{3} +\frac{6\sqrt{5} }{7} = \frac{7+18\sqrt{5} }{21}[/tex]
which is an irrational number because fraction include √5 also.
Thus, Jacob is not correct.
