Question

expand
$( \sqrt{3} + 1) ^{2}$
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Answer 1

Given:

• Square of a Irrational number is given to us.

To Find:

• The expanded value of the number.

Concept Used:

• We will use the formula of (a+b)².

Answer:

Here its given square of a irrational number which is (√3+1)².

We will be using

• ☞ (a+b)²=a²+b²+2ab.

Using above identity ,

= (√3+1)²

=(√3)²+(1)²+2×1×√3.

=3+1 +2√3 .

=4+2√3.

Hence the expanded value is 4+2√3.

Some more identities:

☞(a+b)²=a²+b²+2ab = (a-b)²+4ab.

☞(a-b)²=a²+b²-2ab =(a+b)²-4ab.

☞a²-b²=(a+b)(a-b)

☞(a-b)³= a³-b³-3ab(a-b)

☞(a+b)³= a³+b³+3ab(a+b)

☞a³+b³=(a+b)(a²-ab+b²)

☞a³-b³=(a-b)(a²+ab+b²)