The number 3 - -3 3 - -3 is a-an -

The correct option is B all of these (3 √(3)) (3 + √(3)) Using equation, (a+b)(a b)=a^2 b^2 3^2 (√(3))^2=9 3=6 the final number is not square root, s ...

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Standard XII

Mathematics

General Term of Binomial Expansion

The number ...

Question

The number $(3 - \sqrt{3}) (3 + \sqrt{3})$ is a/an .........

rational number

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natural number

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real number

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all of these

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Solution

The correct option is B all of these
$(3 - \sqrt{3}) (3 + \sqrt{3})$
Using equation, (a+b)(a-b)=a^2-b^2
$3^{2} - (\sqrt{3})^{2} = 9 - 3 = 6$
the final number is not square root, so all the answers are correct.
Answer (D) all of these

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Similar questions

Q. Examine, whether the following numbers are rational or irrational:

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

Q. The smallest number by which

\sqrt{27}

should be multiplied so as to get a rational number is

(a)

\sqrt{27}

(b)

3 \sqrt{3}

(c)

\sqrt{3}

(d) 3

Q. Fill in the blanks to complete the proof of

1 + 7 \sqrt{3}

as an irrational number, provided

\sqrt{3}

is an irrational number.

Let’s assume

1 + 7 \sqrt{3}

be a rational number

\Rightarrow 1 + 7 \sqrt{3} = \frac{a}{b}, b \neq 0

\Rightarrow \sqrt{3} =

(i)___________ which is a (ii)_________ number.

\Rightarrow \sqrt{3}

is a rational number.
But

\sqrt{3}

is a/an irrational number.
Hence, we have arrived at a contradiction.

∵ 1 + 7 \sqrt{3}

is an irrational number.

$2 \sqrt{3} \times 3 \sqrt{2}$ is a/an ___ number. (rational/irrational)

\sqrt{3}

is

(a) an integer
(b) a rational number
(c) an irrational number
(d) none of these

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The number (3−√3)(3+√3) is a/an .........

The correct option is B all of these(3−√3)(3+√3)Using equation, (a+b)(a-b)=a^2-b^232−(√3)2=9−3=6the final number is not square root, so all the answers are correct.Answer (D) all of these

The number $(3 - \sqrt{3}) (3 + \sqrt{3})$ is a/an .........

The correct option is B all of these
$(3 - \sqrt{3}) (3 + \sqrt{3})$
Using equation, (a+b)(a-b)=a^2-b^2
$3^{2} - (\sqrt{3})^{2} = 9 - 3 = 6$
the final number is not square root, so all the answers are correct.
Answer (D) all of these