Question

simplify (5+root 27) +(4-root 3) -(2 root 3 -root 6 )

Answer 1

$\huge\bold{Question:-}$

$(5 + \sqrt{27} ) + (4 - \sqrt{3} ) - (2 \sqrt{3} - \sqrt{6} )$

$\huge\bold{Solution:-}$

$5 + \sqrt{27} = 5 + \sqrt{9 \times 3}$ $= > 5 + 3 \sqrt{3}$

So,

$5 + 3 \sqrt{3} + 4 - \sqrt{3} - 2 \sqrt{3} - \sqrt{6}$

= $5 + 4 + 3 \sqrt{3} - \sqrt{3} - 2 \sqrt{3} - \sqrt{6}$

= $9 + 3 \sqrt{3} - 3 \sqrt{3} - \sqrt{6}$

= $9 - \sqrt{6}$

Final Answer:-

$9 - \sqrt{6}$

Answer 2

Answer:

=> 9 + √6

Step-by-step explanation:

Given:-

(5 +√27) + (4 - √3) - (2√3 - √6)

To find:-

Simplify

Solution:-

We have,

(5 +√27) + (4 - √3) - (2√3 - √6)

Factor 27 = 3² × 3. Rewrite the square root of the product √(3² × 3) as the product of square roots √3²√3. Take the square root of 3²

→ 5 + 3√3 + 4 -√3 - (2√3 - √6)

Add 5 and 4 to get 9.

→ 9 + 3√3 - √3 - (2√3 - √6)

To find the opposite of 2√3 - √6, find the opposite of each term.

→ 9 + 2√3 - 2√3 - (-√6)

Combine 2√3 and -2√3 to get 0.

→ 9 - (-6)

The opposite of -√6 is√6.

→ 9 + √6 Ans.