Question

find the value of:- √(√2-√3)^2 + √(√2+√3)^2​

Answer 1

Answer:

√(√2 - √3)² + √(√2 + √3)² = 2√2

Step-by-step explanation:

Let √2 = a and √3 = b

We have,

√(√2 - √3)² + √(√2 + √3)²

= √(a - b)² + √(a + b)²

We know that,

Squaring a number and then taking its square root or vice versa is the same number itself.

For ex:- √(4)²

= √16

= 4

∴ √(4)² = 4

Similarly,

√(a - b)² + √(a + b)²

= (a - b) + (a + b)

= a - b + a + b

= 2a

But we said that,

a = √2

2a = 2√2

Hence,

√(√2 - √3)² + √(√2 + √3)² = 2√2

Hope it helped and believing you understood it........All the best