Question

Simplify
(5+√7)(5-√7)

Answer 1

Answer:

(5+$\sqrt{7$) (5-$\sqrt{7$) = 18

Step-by-step explanation:

The formula used here is

(a+b) (a-b)=  $a^{2} - ab+ab- b^{2}$

In which -ab +ab = 0.

So it becomes, (a+b)(a-b)= $a^{2} - b^{2}$.

Apply this formula in (5+$\sqrt{7}$) (5-$\sqrt{7}$) = $5^{2} - \sqrt{7} ^{2}$,     ( a is 5 and b is $\sqrt{7}$ )

= 25- 7     ( as $\sqrt{7}$×$\sqrt{7}$ = 7 )

= 18.

Answer 2

(5 + √7)(5 - √7) = 18

Given :

The expression (5 + √7)(5 - √7)

To find :

Simplify the given expression

Formula :

a² - b² = (a + b) (a - b)

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

(5 + √7)(5 - √7)

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{ (5 + \sqrt{7} )(5 - \sqrt{7}) }$

$\displaystyle \sf{ = {(5)}^{2} - {( \sqrt{7}) }^{2} }$

$\displaystyle \sf{ = 25 - 7}$

$\displaystyle \sf{ = 18 }$

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