Question

(5+√8)+(3-√2)-(√2-6) when simplified

Answer 1

Answer:

14+4√2

Step-by-step explanation:

(5+√8)+(3-√2)-(√2-6)

(5+√2.2.2)+(3-√2)-(√2-6)

5+2√2+3-√2-√2+6

14+2√2-2√2

14

Answer 2

Answer:

The value of (5+√8)+(3-√2)-(√2-6) = 14

Step-by-step explanation:

Given expression is

(5+√8)+(3-√2)-(√2-6)

Solution:

In order to simplify the given expression, we need to first remove the bracket and simplify the integers and surds separately

The prime factorization of 8 = 2×2×2

√8 = $\sqrt{2X2X2} = \sqrt{2^2X2} = 2\sqrt{2}$

Expanding the brackets we get

(5+√8)+(3-√2)-(√2-6) = 5+√8+3-√2-√2+6

Substituting the value of √8 we get

= 5+2√2+3-√2-√2+6

Adding the integers and surds separately

= (5+3 +6) +(2√2-√2-√2)

= 14 + (2√2-2√2)

=14  (since, 2√2-√2-√2 = 0)

∴The value of (5+√8)+(3-√2)-(√2-6) = 14

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