Question

Simplify the given expression, and most importantly show the steps, please.

Answer 1

Given:-

• 6/√8 .

To Do :-

• To simplify the given expression.

Solution:-

We have ;

`\implies (6)/(\sqrt8) \\`

We can write 8 as 2³ . So ,

`\implies (6)/(√(2^3)) \\`

`\implies (6)/(2\sqrt2) \\`

`\implies (3)/(\sqrt2) \\`

Rationalize the denominator by multiplying numerator and denominator by √2 .

`\implies (3\sqrt2)/(\sqrt2.\sqrt2) \\`

`\implies\boxed{ (3\sqrt2)/(2)} \\`

This is given required answer.

and we are done!

Answer 2

(3 sqrt(2))/2

Explanation:

Simplify the following:

6/sqrt(8)

Rationalize the denominator. 6/sqrt(8) = 6/sqrt(8)×(8^(1 - 1/2))/(8^(1 - 1/2)) = (6×8^(1 - 1/2))/8:

(6×8^(1 - 1/2))/8

The gcd of 6 and 8 is 2, so (6×8^(1 - 1/2))/8 = ((2×3) 2 sqrt(2))/(2×4) = 2/2×(3×2 sqrt(2))/4 = (3×2 sqrt(2))/4:

(3×2 sqrt(2))/4

2/4 = 2/(2×2) = 1/2:

Answer: (3 sqrt(2))/2