The correct option is A a natural numberConsider the identity: (a+b)(a b) = (a^2 b^2) (3+√(5))(3 √(5)) =9 5=4, which is rational Hence, the given expression ...

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Byju's Answer

Standard IX

Mathematics

Operations on Irrational Number

3+√53-√5 is r...

Question

$(3 + \sqrt{5}) (3 - \sqrt{5})$ is rational.

a natural number

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an integer

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Solution

The correct option is A a natural number
Consider the identity:

$(a + b) (a - b)$ = $(a^{2} - b^{2})$

$(3 + \sqrt{5}) (3 - \sqrt{5}) = 9 - 5 = 4, which is rational$

Hence, the given expression is rational.

Therefore, the statement is true.

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Similar questions

$(3 + \sqrt{5}) (3 + \sqrt{5})$ is rational.

$(3 + \sqrt{5}) (3 + \sqrt{5})$ is ___.( irrational/rational)

Q. Show that:

(3 + \sqrt{5}) (3 - \sqrt{5})

is a rational number.

Q. set of rational numbers is

{- 6, - 5 \frac{3}{4}, - \sqrt{4}, - \frac{3}{5}, - \frac{3}{8}, 0, \frac{4}{5}, 1, 1 \frac{2}{3}, 3.01, 8.47}

Q. Simpify and express following as a rational number :
i)

{(\frac{6}{5})}^{3} \times {(\frac{5}{2})}^{2}

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(3+√5)(3−√5) is rational.

The correct option is A a natural numberConsider the identity: (a+b)(a−b) = (a2−b2) (3+√5)(3−√5)=9−5=4, which is rational Hence, the given expression is rational. Therefore, the statement is true.

$(3 + \sqrt{5}) (3 - \sqrt{5})$ is rational.

The correct option is A a natural number
Consider the identity:

$(a + b) (a - b)$ = $(a^{2} - b^{2})$

$(3 + \sqrt{5}) (3 - \sqrt{5}) = 9 - 5 = 4, which is rational$

Hence, the given expression is rational.

Therefore, the statement is true.