The number 1-32 is a-an

The correct option is C Irrational Number On expanding (1+√(3))^2 using the formula (a+b)^2, we find that (1+√(3))^2=(1)^2+(√(3))^2+2(1)(√(3)) = 4 + 2√(3) wh ...

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Standard X

Mathematics

Irrational Numbers

The number 1+...

Question

The number ${(1 + \sqrt{3})}^{2}$ is a/an

Natural Number

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Rational Number

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Irrational Number

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Integer

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Solution

The correct option is C
Irrational Number

On expanding ${(1 + \sqrt{3})}^{2}$ using the formula ${(a + b)}^{2}$ , we find that

${(1 + \sqrt{3})}^{2} = {(1)}^{2} + {(\sqrt{3})}^{2} + 2 (1) (\sqrt{3}) = 4 + 2 \sqrt{3}$

which is the sum of a rational term, $4$ and an irrational term $2 \sqrt{3}$ .

Therefore, the equation ${(1 + \sqrt{3})}^{2}$ is also irrational.

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Similar questions

The number $(2 + \sqrt{3}) (2 - \sqrt{3})$ is a/an

Q. The atomic number of an element is

32

and mass number

55

. Calculate the number of neutrons?

Q. The number of positive integers n in the set

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for which the number

\frac{1^{2} + 2^{2} + 3^{2} + . . . . . n^{2}}{1 + 2 + 3 + . . . . . n}

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Q. State True or False:

(\sqrt{2} + \sqrt{3})^{2}

is an irrational number.

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The number (1+√3)2 is a/an

The correct option is C Irrational Number On expanding (1+√3)2 using the formula (a+b)2, we find that (1+√3)2=(1)2+(√3)2+2(1)(√3)=4+2√3 which is the sum of a rational term, 4 and an irrational term 2√3. Therefore, the equation (1+√3)2 is also irrational.

The number ${(1 + \sqrt{3})}^{2}$ is a/an