Math, asked by sonu668485, 1 year ago

which of the following equations are irrational
$(x {}^{2} = 9 )(y { }^{2} = 5)(z {}^{2} = 64)(v {}^{2} = 0.04)$
1)
$x {}^{2} = 9$
2)
$y {}^{2} = 5$
3)
$z {}^{2} = 64$
4)
$v {}^{2} = 0.04$

sonu668485: please answer me guys

Answers

Answered by BrainlyPromoter

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Option ( B )

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Irrational number are one of the categories of real numbers which does not have an exact value and cannot be expressed in a form same as p/q.

Let us solve the equations one by one to find our result.

1) x ^ 2 = 9 => x = √9 => x = 3
Since we have got a rational number as a result, this cannot be the required answer.

2) y ^ 2 = 5 => y = √5
Since we have got an irrational number as a result, this may be our answer but for safe sight we will have a look at other options as well.

3) z ^ 2 = 64 => z = √64 => z = 8
Since we have got a rational number as a result, this cannot be the required answer.

4) v ^ 2 = 0.04 => v = √0.04 => v = 0.2
Since we have got a rational number as a result, this cannot be the required answer.

• At last, since we have a irrational number as the result only in option B, it is the correct answer.

nickkaushiknick: see my solution above when you'll sole square of y = 5, you'll get root 5

sprao534: as per my knowledge is concern a variable under a radical is called irrational equation. you are telling about roots. i am asking about irrational equation. for example Root of( 3x-4)=2

sprao534: is it not irrational equation?

nickkaushiknick: yes, in an equation when variable is under a radical, it is called not a polynomial, in which case it can be defined as irrational equation.

sprao534: it can be can converted into a polynomial by mathematical oparation

nickkaushiknick: ofcourse it can be converted and into a polynomial by squaring both side.... but the solution or root of this equation can not make it a rational number. So it will remain an irrational equation/number

sprao534: the example i had given, after squaring get a root 8/3

sprao534: thanks for giving reply.

nickkaushiknick: yea, put this value in the equation, do you get an irrational/number expression?

naina268: b is correct

Answered by nickkaushiknick

Answer:

y² = 5 is Irrational

Step-by-step explanation:

Here you can see

x² = 9 or

x² - 9 = 0

x² - 3² = 0

(x + 3) ( x - 3) = 0 [∵ a² - b² = (a + b) ( a - b)]

x + 3 = 0 x - 3 = 0

x = -3 x = 3 [Both are rational numbers]

Similarly

y² = 5

y = ± √5 (Since √5 is an irrational number)

∴ Option 2) y² = 5 is irrational

just to check further

z² = 64

z = ±8 (Rational)

and

v² = 0.04

v = ± 0.2 (Rational)

Anonymous: NYC answer

nickkaushiknick: thanks :)

BrainlyPromoter: perfect, definitely deserves approval

nickkaushiknick: thanks :)

sprao534: one doubt :what is irrational equation?

nickkaushiknick: A number which can not be expressed as p/q, where p and q must be integers and q not equals to 0. Like here Root 5 is not an integer so it can not be expressed as p/q where p and q should be integer

sprao534: i am asking about irrational equation but you telling about irrational number.

which of the following equations are irrational 1)2)3)4)

Answers

which of the following equations are irrational
$(x {}^{2} = 9 )(y { }^{2} = 5)(z {}^{2} = 64)(v {}^{2} = 0.04)$
1)
$x {}^{2} = 9$
2)
$y {}^{2} = 5$
3)
$z {}^{2} = 64$
4)
$v {}^{2} = 0.04$