Question

simplify \sqrt { 7 - \sqrt { 13 } } - \sqrt { 7 + \sqrt { 13 } }​

Answer 1

Concept:

The square root is a factor of a number that, when multiplied by itself, gives the original number.

Given:

√(7 - √3) - √(7 + √3)

Find:

We are asked to simplify √(7 - √3) - √(7 + √3).

Solution:

We have,

√(7 - √3) - √(7 + √3)

Now,

Using the identity,

i.e.

(a + b)² = a² + b² + 2ab

So,

Squaring the given term,

i.e.

[√(7 - √3) - √(7 + √3)]²

Now,

[√(7 - √3) ]² + [√(7 + √3)]² - 2 × √(7 - √3)  × √(7 + √3)

On solving we get,

7 - √3 + 7 + √3 - 2 × √46

Now,

Cancelling out √3,

We get,

14 - 2√46

Hence, the simplified form of √(7 - √3) - √(7 + √3) is 14 - 2√46.

#SPJ1

Answer 2

Answer:

2

Step-by-step explanation:

Given:- The given expression √(7 - √13 )  - √(7 + √13 ) .

To Find:- Value of the above expression.

Solution:-

(√(7 - √13 ))-(√(7 + √13 ))

Using the formula (a - b)² = a² + b² - 2ab

= ((√(7 - √13 ))-(√(7 + √13 )))²

= (√(7 - √13 ) )² + (√(7 + √13 ) )² - 2(√(7 - √13) )(√(7 + √13) )

= 7 - √13 + 7 + √13 - 2(√(7² - √13² ) )

= 14 - 2(√(49 - 13) )

= 14 - 2√36

= 14 - 2 × 6

= 14 - 12

= 2

Therefore, the value of expression √(7 - √13 )  - √(7 + √13 ) is 2.

#SPJ2

https://brainly.in/question/40538017

https://brainly.in/question/2743476