How do you simplify √20d+4√12d−3√45d?

2 Answers
EZ as pi
Aug 15, 2017

=8√3d−7√5d

Explanation:

Write each radicand as the product of its factors and try to find squares wherever possible:

√20d+4√12d−3√45d

=√4×5d+4√4×3d−3√9×5d ← find the roots

=2√5d+4×2√3d−3×3√5d

=2√5d+8√3d−9√5d ← collect like terms

=8√3d−7√5d

Johnny L.
Aug 15, 2017

After simplifying, you are left with 8√3d−7√5d

Explanation:

First, let's simplify the numbers under the square root.

√20

This can be rewritten as √4⋅5

4 has a square root, so we can pull its square root out of the radical, giving us 2√5

Now we do the same thing to √12 and √45

√12=√4⋅3=2√3

√45=√9⋅5=3√5

We can't do much with the √d, so at this point we have:

2√5d+4⋅2√3d−3⋅3√5d

After multiplication, we have:

2√5d+8√3d−9√5d

We have two √5d terms, so we can combine them, giving us the final answer of:

8√3d−7√5d

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