Question

If x^2 = 7, y^2 = 25, z^2 = 0.09, u^3 = 343, which one out of x, y, z, u is irational​

Answer 1

SOLUTION

GIVEN

x² = 7, y² = 25, z² = 0.09, u³ = 343

TO DETERMINE

which one out of x, y, z, u is irrational

CONCEPT TO BE IMPLEMENTED

Rational Number

A Rational number is defined as a number of the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

EVALUATION

Here it is given that

x² = 7, y² = 25, z² = 0.09, u³ = 343

We simplify all as below

x² = 7

⇒ x = √7

So x can not be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So x is irrational

y² = 25

$\implies \sf{y = \pm \: 5}$

So y can be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So y is rational

z² = 0.09

$\implies \sf{z = \pm \: 0.3}$

So z can be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So z is rational

u³ = 343

⇒ u = 7

So u can be written in the form $\displaystyle \sf{ \frac{p}{q} \: }$

Where p & q are integers with q ≠ 0

So u is rational

FINAL ANSWER

Hence x is irrational

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