Question

MULTIPLE CHOICE QUESTION

The product of (SQUARE ROOT SIGN)576 and (SQUARE ROOT SIGN) 684 is
(1) irrational because both factors are irrational
(2) rational because both factors are rational
(3) irrational because one factor is irrational
(4) rational because one factor is rational

Answer 1

The given expression is irrational because one factor is irrational

Explanation:

Answer 2

The given expression is irrational because one factor is irrational

Explanation:

Given the expression

`(√(576))(√(684))`

we have to find that the product is rational or irrational.

`√(576)=√(26* 26)=26`

`√(684)=√(2 * 2 * 3 * 3 * 19)=2* 3√(19)=6√(19)`

`\text{The square root of 19 is irrational }`

`\text{The square root of 684 is irrational }`

Hence, the first factor of the expression is rational and the second factor is irrational therefore the product is irrational.

∴ option 3 is correct

The given expression is irrational because one factor is irrational