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Need Help Please Explain I'm confused

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User Nobwyn
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1 Answer

5 votes
OK. Quite a bit of work for 5 points, but here goes:

Picture on the left:

When square roots need to be multiplied, just go ahead and
mash everything together.

The product of √one thing) times (√another thing

is just √(one thing times the other thing) .

So √(3x²y³) · 2 · √(72x³y⁴) is just

2 · √(3x²y³ · 72x³y⁴)

= 2 · √(216 x⁵ y⁷)

That looks pretty complicated. But if you break it up into things that are
perfect squares, then you can pull those out of the square root.

2 · √(216 x⁵ y⁷)

= 2 · √(6·36 · x⁴·x · y⁶·y)

The bold things are perfect squares, so take their square roots
and write those outside of the square root sign.

= 2 · √(6·36 · x⁴·x · y⁶·y)

= 2 · 6 · x² · y³ · √(6 · x · y)

= 12 x² y³ √6xy .
________________________________________________

Middle picture:

How do you take the 8th root of something raised to a power ?
Just divide the power by 8 .

⁸√(p²⁰· q²⁹ · r¹¹)

= ⁸√(p¹⁶·p⁴ · q²⁴·q⁵ · r⁸·r³)

= p² q³ r ⁸√p⁴ q⁵ r³
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Picture on the right:

-3i (6 + 2i)

= (-3i)·(6) + (-3i)·(2i)

= -18i + -6i²

If ' i ' = √-1 , then i² = -1 .

-18i + -6i²

= -18i + -6(-1)

= -18i + 6 .

Make it a little bit neater. Factor out the ' 6 ':

-18i + 6

= 6·(-3i + 1) .
User Alexander Rakhmaev
by
8.0k points

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