How do you simplify 3sqrt50*sqrt22?

3 Answers
Serena D.
May 5, 2018

30sqrt11

Explanation:

3sqrt50*sqrt22

3sqrt(25*2)*sqrt22 rarr 25 is a perfect square and can be taken out of the radical

3*5sqrt2*sqrt22

15sqrt2*sqrt22

15sqrt(2*22)

15sqrt44

15sqrt(4*11) rarr 4 is a perfect square

15*2sqrt11

30sqrt11

Please delete this acccount. Thanks!
May 5, 2018

I'm going to try to write out your question mathematically:
root(3)(50xxsqrt22)

Explanation:

To solve this exceedingly complicated question, let's start by converting everything into indices.

But first, we should simplify your equation:
root(3)(sqrt55000)
Now the question will be written in indicial form as:
(55000^(1/2))^(1/3)

By the power law of indices -> (a^m)^n=a^(mn), this would make the indices 1/2xx1/3=1/6.
Therefore, the question will now become:
55000^(1/6)
=root(6)55000
=50root(6)22
In surd form.

I hope this helps!

Barney V.
May 5, 2018

30sqrt11

Explanation:

3sqrt50*sqrt 22

:.=3 sqrt(2*5*5)*sqrt(2*11)

:.=sqrt 5*sqrt 5=5

:.=3*5 sqrt 2*sqrt 2*sqrt 11

:.=15 sqrt 2*sqrt 2*sqrt 11

:.=sqrt2*sqrt2=2

:.=2*15*sqrt 11

:.=30 sqrt11

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