Question

simplify 5√2+2√8-3√32+4√128​

Answer 1

$\huge\bold{ANSWER~:}$

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$= 5 \sqrt{2} + 2\sqrt{8} - 3\sqrt{32} + 4 \sqrt{128} \\ \\ = 5 \sqrt{2} + 2 \sqrt{4 \times 2} - 3 \sqrt{16 \times 2} + 4 \sqrt{64 \times 2} \\ \\ = 5 \sqrt{2} + 4 \sqrt{2} - 12 \sqrt{2} + 32 \sqrt{2} \\ \\ = \sqrt{2} (5 + 4 - 12 + 32) \\ \\ = 29 \sqrt{2}$

${\huge\color{Red}{Answer~is~29\sqrt{2}~. }}$

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Answer 2

$5 \sqrt{2} + 2 \sqrt{8} - 3 \sqrt{32} + 4 \sqrt{128}$

2√8=2√2×2×2=2×2√2

2√8=4√2

3√32=2√2×2×2×2×2

=3×2×2√2

=12√2

4√128=4√2×2×2×2×2×2×2

=4×2×2×2√2

=32√2

Now All Terms Can Written as

$5 \sqrt{2} + 4 \sqrt{2} - 12 \sqrt{2} + 32 \sqrt{2}$

As We know When There is Like terms like √2 in These Terms

If

a√x+b√x=a+b√x

a√x-b√x=a-b√x

Now,

$5 \sqrt{2} + 4\sqrt{2} + 32 \sqrt{2} - 12 \sqrt{2} \\ \\ 41 \sqrt{2} - 12 \sqrt{2} \\ \\ = 29 \sqrt{2}$

Answer=29√2