Which expressions below equal a rational number? Choose all that apply. 4/5 + 3/8; sqrt(100) + sqrt(5); 7sqrt(5) - sqrt(245); (4sqrt(7))(2sqrt(7)); pi * sqrt(36)
Answers
Given : Few expressions
To Find : Which expressions below equal a rational number
4/5 + 3/8
√100 + √5
7√5 - √245
(4√7)(2√7)
π * √36
Solution:
Rational numbers p/q form where p and q are integers and q ≠ 0.
All other real numbers are irrationals
4/5 + 3/8 is a rational number
as sum of two rational numbers is always rational
√100 + √5
= 10 + √5 is an irrational number as sum of rational and irrational number is always irrational
7√5 - √245
= 7√5 - 7√5
= 0 is a rational number
(4√7)(2√7)
= 56
rational number
π * √36
= 6π is irrational as product of non zero rational and irrational number is always irrational number
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Given :- Which expressions below equal a rational number ? Choose all that apply.
A) 4/5 + 3/8
B) sqrt(100) + sqrt(5)
C) 7sqrt(5) - sqrt(245)
D) (4sqrt(7))(2sqrt(7))
E) pi * sqrt(36)
Solution :-
numbers which can be written in the form of p/q where q ≠ 0 are called rational numbers .
so, checking all one by one we get,
A) 4/5 + 3/8
→ 4/5 + 3/8
→ (32 + 15) /40
→ 47/40
comparing with p/q,
→ p = 47
→ q = 40 which is not equal to 0 .
so,
→ 47/40 = Rational number .
B) √100 - √5
→ 10 - √5
since we know that, if a square root is not a perfect square, then it is considered an irrational number .
so,
→ Rational - irrational = irrational number .
C) 7√5 - √245
→ 7√5 - 7√5
→ 0
→ 0/1
since q ≠ 0,
→ 0/1 = Rational number .
D) 4√7 * 2√7
→ 8 * 7
→ 56 = Rational number .
E) π * √36
→ π * 6
since π is an irrational number .
→ irrational * rational = Irrational number .
Therefore, (A) , (C) and (D) are rational numbers .
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