Question

Give two examples of irrational numbers whose square is an irrational number.

Answer 1

Answer:

Common Examples of Irrational Numbers

Pi, which begins with 3.14, is one of the most common irrational numbers. ...

e, also known as Euler's number, is another common irrational number. ...

The Square Root of 2, written as √2, is also an irrational number.

Answer 2

Answer:

Examples of two irrational numbers whose square is an irrational number are  $2+\sqrt{3}$ and $\sqrt{2} +\sqrt{5}$

Step-by-step explanation:

Recall the concept:

Rational numbers are the numbers that can be expressed in the form $\frac{p}{q}$, where 'p' and 'q' are integers and q≠0

Some examples of rational numbers are $\frac{11}{12} ,\frac{3}{4}$, 2,100,4.86

Irrational numbers are the numbers that can not  be expressed in the form $\frac{p}{q}$, where 'p' and 'q' are integers and q≠0

Some examples of irrational numbers are $\sqrt{2} ,\frac{8}{\sqrt{5} } ,2+\sqrt{3}$

Solution:

Required to find two irrational numbers whose square is an irrational number

1. $2+\sqrt{3}$

$(2+\sqrt{3})^2 = 2^2 +(\sqrt{3} )^2+2X2\sqrt{3} = 4+3+4\sqrt{3} = 7+4\sqrt{3}$, which is an irrational number

    2.   $\sqrt{2} +\sqrt{5}$

$(\sqrt{2} +\sqrt{5} )^2 = (\sqrt{2} )^2 +(\sqrt{5} )^2 +2 X \sqrt{2} X\sqrt{5}$ = 2+5+2$\sqrt{10}$ = 7+2$\sqrt{10}$, which is an irrational number

∴Examples of two irrational numbers whose square is an irrational number are  $2+\sqrt{3}$ and $\sqrt{2} +\sqrt{5}$

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