2√5 . it is retional number
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Answer:
Step-by-step explanation:
No it’s and irrational number!
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0
Answer:
2√5 is an irrational because √5 is irrational. The only way you can add or subtract a number to √5 to make the result rational, is by keeping the number irrational.
Step-by-step explanation:
Use proof by contradiction. Assume that the sum is rationial, that is
2–√+5–√=ab
where a and b are integers with b≠0. Now rewrite this as
5–√=ab−2–√.
Squaring both sides of this equation we obtain
5=a2b2−22–√ab+2.
Now, carefully solve for 2–√ and obtain
2–√=−3b2a+a2b.
This implies that 2–√ is a rational number which is a contradiction. Thus
2–√+5–√
is an irrational number.
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