Question

is the number (3- root 7) (3+ root 7) rational or irrational and how?

Answer 1

it is rational no. bcoz when we multiply it.
the property will come in it (a+b)(a-b) = a2 - b2
3ka sq - underroot 7 ka sq
9-7 = 2
ans which is rational
hope u get it
plz mark as brainlient

Answer 2

The number (3 + √7)(3 - √7) is a rational number as the number can be written in form p/q where p & q are integers with q ≠ 0

Given :

The number (3 + √7)(3 - √7)

To find :

Is the number (3 + √7)(3 - √7) rational or irrational and how ?

Solution :

Step 1 of 3 :

Write down the given number

Here the given number is (3 + √7)(3 - √7)

Step 2 of 3 :

Simplify the given number

(3 + √7)(3 - √7)

= (3)² - (√7)²

= 9 - 7

= 2

Step 3 of 3 :

Check the number is rational or irrational

(3 + √7)(3 - √7) = 2

Now 2 can be rewritten as 2/1

Which is of the form p/q where p = 2 , q = 1 are integers with q ≠ 0

So the number (3 + √7)(3 - √7) can be the form p/q where p & q are integers with q ≠ 0

Now we know that Rational number is defined as a number of the form p/q where p & q are integers with q ≠ 0

Hence the number (3 + √7)(3 - √7) is a rational number

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