The expression [tex](7+\sqrt{3})^{2} + (7-\sqrt{3})^{2}[/tex] is rational.
Given:
[tex](7+\sqrt{3})^{2} + (7-\sqrt{3})^{2}[/tex]
To Find:
the given expression is rational or irrational.
Solution:
We can find the solution to this problem through the following concepts and simplification as stated under.
(Rational number by its characteristic feature can be expressed as the fraction or the ratio of two integers such that the denominator of the fraction has non-zero value.)
(Irrational number cannot be rewritten in the form of fraction or ratio of two integers and are non-terminating as well as non-repeating.)
Let us suppose we have two integers p,q; a rational number R and an irrational number N.
Mathematically we can express in the following way
Answers & Comments
Verified answer
The expression [tex](7+\sqrt{3})^{2} + (7-\sqrt{3})^{2}[/tex] is rational.
Given:
[tex](7+\sqrt{3})^{2} + (7-\sqrt{3})^{2}[/tex]
To Find:
the given expression is rational or irrational.
Solution:
We can find the solution to this problem through the following concepts and simplification as stated under.
(Rational number by its characteristic feature can be expressed as the fraction or the ratio of two integers such that the denominator of the fraction has non-zero value.)
(Irrational number cannot be rewritten in the form of fraction or ratio of two integers and are non-terminating as well as non-repeating.)
Let us suppose we have two integers p,q; a rational number R and an irrational number N.
Mathematically we can express in the following way
[tex]R=\frac{p}{q}, q\neq 0\\N\neq \frac{p}{q}[/tex]
Now we shall focus on simplification as under.
[tex](7+\sqrt{3})^{2} + (7-\sqrt{3})^{2}\\=7^{2} +2\times7\times\sqrt{3}+(\sqrt{3})^{2}+7^{2} -2\times7\times\sqrt{3}+(\sqrt{3})^{2}\\=2\times[7^{2} +(\sqrt{3})^{2} ]\\=2\times(49+3)\\=2\times52\\=104\\=\frac{104}{1}[/tex]
The obtained answer is in the form of a rational number which indicates that the expression is rational in nature.
The required answer is that the expression [tex](7+\sqrt{3})^{2} + (7-\sqrt{3})^{2}[/tex] is rational and hence is not an irrational number.