Answer :
The answer is irrational. Any irrational number doubled is still irrational.
Sum of 3√2 and 4√2 is an irrational number.
What are irrational numbers?
" Irrational numbers are those numbers which cannot be written in fraction or rational form."
According to the question,
Suppose 3√2 + 4√2 be a rational number.
which can be expressed in form of (p / q) form such that 'q' does not divides 'p'
3√2 + 4√2 = (p / q)
⇒ 7√2 = ( p / q)
Squaring both the sides we get,
49 × 2 = ( p² / q² )
⇒ 2 ×(49q²) = p²
⇒ p is an even number
⇒p = 2k , k≠0
Therefore,
2 × ( 49q²) = (2k)²
⇒2×(49q²) = 4k²
⇒q² = (2k² / 49)
Both p and q are even which implies 'q' divides 'p'.
It is contradictory to our supposition,
Therefore, 3√2 + 4√2 is an irrational number.
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