Question

Can someone help me out with these equations?

1. (5+ √3)^2
2. (√6-5√3)^2
3. (6+3√2)^2

Answer 1

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Answer:

1. 28 +10√3
2. 81 -30√2
3. 54 +36√2

Explanation:

It is useful to remember the form for the square of a binomial.

(a +b)² = a² +2ab +b²

(a -b)² = a² -2ab +b²

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1. (5 +√3)² = 5² +2·5·√3 +(√3)² = 25 +10√3 +3

= 28 +10√3

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2. (√6 -5√3)² = (√6)² -2·√6·5√3 +(5√3)² = 6 -30√2 +75

= 81 -30√2

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3. (6 +3√2)² = 6² +2·6·3√2 +(3√2)² = 36 +36√2 +18

= 54 +36√2