Respuesta :
The smallest value of n such that the expressions √ (76+n) and √( 2n+26) become rational will be 5.
What is an irrational number?
Any real number that cannot be written as the quotient of two integers, p/q, where p and q are both integers, is referred to as an irrational number.
In another word, irrational numbers are those numbers that can not terminate.
For example, √2, and √3 are irrational numbers because they cannot be written as p/q where p and q both should be integers.
Given the expressions
√ (76+n) and √( 2n+26)
Now to be the expression it is rational the value inside the under root should become a perfect square. Because all under-root values are irrational.
So to be a perfect square the value nearest to 76 is 81 which is 9².
So,
√ (76+n) = √ 81
76 + n = 81 ⇒ n = 81 - 76 = 5
Now,
√ (76+5) ⇒ √ (81) = 9 (rational)
√( 2×5 + 26) = √(36) = 6 (rational)
Hence "The smallest value of n such that the expressions √ (76+n) and √( 2n+26) become rational will be 5".
For more about the irrational number,
https://brainly.com/question/4031928
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