Question

If x^2= 5+2root over 6,
Then what is the value of x?

Answer 1

Answer:

√3 + √2

Step-by-step explanation:

⇒ x^2 = 5 + 2√6

⇒ x^2 = 3 + 2 + 2√6

⇒ x^2 = (√3)² + (√2)² + 2(√3√2)

Using, a² + b² + 2ab = (a + b)²

⇒ x^2 = (√3 + √2)²

⇒ x = √3 + √2

For solving these such problems, what you need to do just to factorise the term under root, such that the sum of those parts becomes equal to other term. (here, 2 + 3 = 5)

Answer 2

Given

• x² = 5 + 2√6

To find

• x

Solution

• x² = 5 + 2√6

This can be written as 3 + 2 + 2√6

• Then x² = √3² + √2² + 2(√3√2)

Then we observe an identity,

• a² + b² + 2ab = (a + b)²

• Hence, x² = (√3 + √2)²

Square cancel,

• x = √3 + √2