Question

सरल कीजिए।
(5 + √7) x (5 – √7)​

Answer 1

Given :-

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

To :-

Evaluate it

Solution :-

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

→ $\sf \: 25 - 7$

→ $\sf 18 \: ans$

Procedure :-

→ This Question is from the number system.

→ In this question we have to find the answer by using square roots identity which is (a+√b)(a-√b) = a² - b².

→ In place of a we will take 5 and in place of b we will take √7 and then we will do the square of both and then we will subract them.

→ The square of 5 will be 25 and the square of √7 will be 7, how? when we will multiply √7 with √7 it will give √49 as the product and 7 is the answer of √49, therefore we will 7.

→ Then we will subract 7 from 25 which will be our final answer which is 18.

Other square root identities :-

1. $\sqrt{ab} = \sqrt{a} \sqrt{b}$

2. $\sqrt{ \frac{a}{b}} = \frac{ \sqrt{a} }{ \sqrt{b} }$

3. $( \sqrt{a} + \sqrt{b})( \sqrt{a} - \sqrt{b}) = a - b$

4. $(a + \sqrt{b})(a - \sqrt{b}) = {a}^{2} - b$

5. ${( \sqrt{a} + \sqrt{b})}^{2} = {a}^{2} + 2 \sqrt{ab} + {b}^{2}$

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Answer 2

Answer:

(5 + √7) x (5 – √7) = 18

Step-by-step explanation:

The given expression is (5 + √7) x (5 – √7)​

Required to simplify the given expression.

Solution:

Recall the formula

1. (a+b)(a-b) =  a² - b²
2. (√a)²  = a

Substitute the value of 'a' = 5 and 'b' = √7 in the equation (1)

(5 + √7) x (5 – √7)​ = 5² - (√7)² = 25 - 7 = 18

∴(5 + √7) x (5 – √7) = 18

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